C₈×#322 #94851

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₈² · Schur multiplier (H₂) = C₄²×C₈

Aliases

634 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 2047);