C₃×#235 #3818

order	144
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂²×D₃×D₄ (order 192) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₃²×C₄ ⋊ C₂
Sylow	C₃² ⋊ #41

88 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 161);