Database of Soluble Groups

The database solgps contains pc-presentations of soluble groups
constructed by S.P. Glasby and translated from Cayley into Magma by
S. Collins. It contains 13 functions G1, G2, ..., G11, B26, F2332
which construct the groups described below. This description dates
from January 1994. After

	load solgps;

the group designated NAME is created by typing

	G := NAME();

G1		The group BO.7^(2+1).13^(14+1) of order 2^4 * 3 * 7^3 * 13^15
		where BO is the binary octahedral group of order 48 and
		7^(2+1) and 13^(14+1) denote extraspecial groups of prime
		exponent.
G2		S4.2^5 of order 768.
G3		A group of order 2^11*3^13 and derived length 8. See
		S.P. Glasby and R.B. Howlett, Extraspecial towers and Weil
		representations, J. Algebra (1992), 236-260 for more details.
G4		S3 wr S3 where |G| = 2^4*3^4 and degree 9.
G5		GL(2,3).3^2.5^9 where |G| = 2^4*3^3*5^9.
G6		S4 wr S4 wr S4 where |G| = 2^63*3^21 and degree 4^3.
G7		Aut(F).F*.F+ where F=GF(2^11). |G| = 11*23*89*2^11.
G8		Aut(F).F*.F+ where F=GF(3^10). |G| = 2^4*5*11^2*61*3^10.
G9		The Borel subgroup of GL(5, 3) which has order 2^5*3^10.
G10		The Borel subgroup of GL(4, 8) which has order 2^18*7^4.
G11		The group Aut(F).F*.F+ where F=GF(2^13). |G| = 13*8191*2^13.
B26		The two generator Burnside group B(2,6) of exponent 6 and
		order 2^28*3^25.
F2332		If F denotes the free group of rank 2, then this is a
		pc-presentation for the group G = F/(F^2)^3 x F/(F^3)^2 of
		exponent 6 and order 2^30*3^28. The subgroup
		<G.1*G.4*G.28*G.31,G.2*G.6*G.29*G.32*G.58> is a 2-generator
		subgroup of exponent 6 and order 2^28*3^25, and hence it is
		B(2,6): a pc-presentation for B(2,6) may be found above in
		function B26. <G.1,...,G.27> and <G.28,...,G.58> are its
		two direct factors.

For example,

	> G := G2();

	Constructing a group G = S4.2^5 of order 768.

	A group with factorized order [ <2, 8>, <3, 1> ]
	has been constructed

Loading solgps defines G2, which hides the G2(q) matrix-group
constructor for the rest of the session; typing G2(q) fails until
"delete G2;" is run.
