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C₃×C₈×Dic₃ #63599

order	288
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₃×C₈×Dic₃

Splittings

derived	C₃ ⋊ C₃×C₄×C₈
Sylow	C₃² ⋊ C₄×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₃
commutator, hypocenter	C₃	C₃×C₄×C₈
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₂×C₃²×C₈	C₂
socle, prime radical	C₂²×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈

99 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₃×C₃⋊C₁₆, #10589103, Dic₃⋊(C₃⋊C₁₆), …
maximal normal subgroup of	Dic₃×C₃⋊C₁₆, #10589103, Dic₃⋊(C₃⋊C₁₆), …
maximal quotient of	C₃×C₈×C₃⋊C₈, C₃×#4454, C₃×Dic₃×C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 247);