C₄×#3295 #6384073

order	512
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2626 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 20 points:

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

maximal subgroup of	C₄×#61451, #72279888, #72279954, …
maximal normal subgroup of	C₄×#61451, #72279888, #72279954, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6291269);