C₃×#798 #63584

order	288
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂³×C₄×D₃ (order 192) · Inn(G) = C₂×D₃ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

Fitting	C₃²×C₁₆ ⋊ C₂
Sylow	C₃² ⋊ M₃₂

57 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 232);