C₂²×C₄²×Q₈ #7625204

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄² · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

C₂²×C₄²×Q₈

15210 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

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

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

320 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂²×C₄×#550, C₂²×#34934, C₂²×#36592, …
maximal normal subgroup of	C₂²×C₄×#550, C₂²×#34934, C₂²×#36592, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532400);