C₂×C₄×#346 #492823

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₈ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

1282 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400019);