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A₄×Dic₉ #88619

order	432
isoclinism	isoclinic class of A₄×D₉
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

A₄×Dic₉

Splittings

C₂²×C₉ ⋊ C₃×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂	A₄×D₉
commutator, hypocenter	C₂²×C₉	C₃×C₄
Frattini	C₂×C₃	D₃×A₄
Fitting, cosocle	C₂³×C₉	C₂×C₃
socle	C₂³×C₃	C₃×D₃
prime radical	C₂×C₃×A₄	D₃
LCS	G ▷ C₂²×C₉
UCS	C₁ ◁ C₂

65 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	S₄×Dic₉, (C₉⋊S₄)⋊C₄, #11722243, …
maximal normal subgroup of	S₄×Dic₉, (C₉⋊S₄)⋊C₄, #11722243, …
maximal quotient of	A₄×C₉⋊C₈, SL(2,𝔽₃)×Dic₉, #11720753, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 266);