Dic₃×C₃⋊C₈ #63552

order	288
isoclinism	isoclinic class of D₃²
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₃² ⋊ C₄×C₈

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃²
commutator, hypocenter	C₃²	C₄×C₈
Fitting, cosocle	C₂×C₃²×C₄	C₂²
socle, prime radical	C₂²×C₃²	C₂×C₄
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄

99 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 200);