C₄×#3444 #7625260

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹³

Aliases

9334 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 6 generators on 20 points:

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

maximal subgroup of	C₄×#21415, #72239493, #72239495, …
maximal normal subgroup of	C₄×#21415, #72239493, #72239495, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532456);