C₃×#809 #63595

order	288
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₃²×C₄⋊C₄ ⋊ C₂
Sylow	C₃² ⋊ #102

113 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 243);