C₃×C₄×C₈² #10626445

order	768
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1572864
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄²×C₈

Aliases

C₃×C₄×C₈²

750 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 768

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 826);