C₂³×#430 #10574087

order	512
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

10714 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 6 generators on 22 points:

(1,2);(3,4);(5,6);(7,8,11,14,12,15,10,20)(9,16,19,21,17,22,18,13);(7,9,10,18,12,17,11,19)(8,13,14,16,15,21,20,22);(9,17)(13,21)(16,22)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481283);