C₂²×C₃⋊C₈ #920

order	96
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×D₃×#5934 (order 2304) · Inn(G) = D₃ · Out(G) = C₂×#5934
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₃⋊C₈

C₃ ⋊ C₂²×C₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 127);