#67⋊C₄ #881

order	96
automorphism	Aut(G) = C₂⁶×D₃ (order 384) · Inn(G) = C₂²×D₃ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₃×C₂²⋊C₄ ⋊ C₂
Sylow	C₃ ⋊ C₄×D₄

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 11 points:

(1,2,3)(4,5,6,7)(9,11);(8,9)(10,11);(2,3)(9,11)

Polycyclic presentation:

2^5,3|c^2=d,b^a=be,f^a=f^2,c^b=ce

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 88);