C₃×#822 #63608

order	288
isoclinism	isoclinic class of #213
automorphism	Aut(G) = C₂³×D₃×D₄ (order 384) · Inn(G) = #67 · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃² ⋊ #108

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(4,5,6)(7,18,11,9,12,20,10,19)(8,17,15,13,16,22,14,21);(5,6)(7,15,10,8,12,14,11,16)(9,21,20,17,19,13,18,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 256);