C₂×C₄⋊C₄×#41 #7625352

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

12322 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 6 generators on 18 points:

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

maximal subgroup of	C₂×C₄×D₄×#41, C₂×#7629681, C₂×#41×#121, …
maximal normal subgroup of	C₂×C₄×D₄×#41, C₂×#7629681, C₂×#41×#121, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532548);