order	144
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂×D₃×AGL(1,ℤ/8) (order 384) · Inn(G) = D₁₂ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₂₄

Splittings

Fitting	C₃²×C₈ ⋊ C₂
Sylow	C₃² ⋊ D₈

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 72);