C₂×#624 #3806

order	144
isoclinism	isoclinic class of D₃²
automorphism	Aut(G) = #72241543 (order 2304) · Inn(G) = D₃² · Out(G) = B(4,𝔽₂)
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₃² ⋊ C₂²×C₄

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 149);