C₄×#2048 #359159

order	512
nilpotency class	3
isoclinism	isoclinic class of #2048
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1479 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

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

maximal subgroup of	C₄×#24472, #72312212, #72312228
maximal normal subgroup of	C₄×#24472, #72312212, #72312228

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 266355);