D₃×#41 #1008

order	96
automorphism	Aut(G) = C₂²×D₃×S₄ (order 576) · Inn(G) = C₂²×D₃ · Out(G) = C₂²×D₃
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₃×#41 ⋊ C₂
Sylow	C₃ ⋊ C₂×#41

164 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 4 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 215);