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C₂×D₃×C₃⋊C₈ #63812

order	288
isoclinism	isoclinic class of D₃²
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₃×C₃⋊C₈

Splittings

C₃² ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃²
commutator, hypocenter	C₃²	C₂²×C₈
Frattini	C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄	C₂²
socle	C₂²×C₃²	C₂×C₄
prime radical	C₂²×C₃×D₃	C₄
cosocle	C₃²×C₄	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄

163 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×D₃×C₃⋊C₈, D₃×#803, #10590318, …
maximal normal subgroup of	C₄×D₃×C₃⋊C₈, D₃×#803, #10590318, …
maximal quotient of	#10590248, C₃⋊C₈×Dic₆, #10590250, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 460);