C₄⋊(C₃⋊C₈) #804

order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×D₃×#120 (order 384) · Inn(G) = C₂×D₃ · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₄⋊(C₃⋊C₈)

C₃ ⋊ C₄⋊C₈

38 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 15 points:

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

Polycyclic presentation:

2^5,3|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 11);