C₂×#626 #3808

order	144
isoclinism	isoclinic class of #625
automorphism	Aut(G) = D₃²×#120 (order 1152) · Inn(G) = D₃² · Out(G) = #120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₃² ⋊ C₂×D₄

124 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 151);