C₂×C₄×#430 #6369924

order	512
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

3182 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 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)

maximal subgroup of	C₄×#60182, #72224744, #72226660, …
maximal normal subgroup of	C₄×#60182, #72224744, #72226660, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277120);