C₃×#805 #63591

order	288
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂³×D₃×D₄ (order 384) · Inn(G) = D₁₂ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₃²×C₄² ⋊ C₂
Sylow	C₃² ⋊ #104

103 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 239);