C₄×D₃² #3800

order	144
isoclinism	isoclinic class of D₃²
automorphism	Aut(G) = C₂×#64241 (order 576) · Inn(G) = D₃² · Out(G) = C₂×D₄
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₄×D₃²

Fitting	C₃²×C₄ ⋊ C₂²
derived, Sylow	C₃² ⋊ C₂²×C₄

116 conjugacy classes of subgroups.

minimal degree	μ(G) = 10
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 3 generators on 10 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 143);