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C₂×D₃×C₃⋊Dic₃ #89027

order	432
isoclinism	isoclinic class of D₃×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂×D₃×C₃⋊Dic₃

Splittings

C₃³ ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂²×C₄
Frattini	C₂	C₂×D₃×C₃⋊D₃
Fitting, socle	C₂²×C₃³	C₂²
prime radical	C₂²×C₃²×D₃	C₂
cosocle	C₂×C₃³	C₂³
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂²

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 15 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₂×D₃)⋊#622, D₃×Dic₃², D₃×(C₂×D₃)⋊Dic₃, …
maximal normal subgroup of	(C₂×D₃)⋊#622, D₃×Dic₃², D₃×(C₂×D₃)⋊Dic₃, …
maximal quotient of	C₂×D₃×C₃⋊(C₃⋊C₈), D₃×#3748, #11723349, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 674);