C₄×#1334 #128536

order	512
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

460 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4);(5,6,7,9,8,10,11,12)(14,18,19,26)(15,21)(16,24)(20,22,25,27)(23,28);(13,14,17,19)(15,22,23,27)(16,25,24,20)(18,21,26,28)

maximal subgroup of	#72343991, #72343996, #72343997
maximal normal subgroup of	#72343991, #72343996, #72343997

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 35732);