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Dic₃×Dic₉ #88440

order	432
isoclinism	isoclinic class of D₃×D₉
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

Splittings

C₃×C₉ ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₉
commutator, hypocenter	C₃×C₉	C₄²
Frattini	C₂²×C₃	D₃²
Fitting, cosocle	C₂²×C₃×C₉	C₂²
socle, prime radical	C₂²×C₃²	C₂×D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂²

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3)(5,7)(6,10)(8,9)(11,12)(17,18,19,20);(2,3)(4,12,7,10,9,8,6,5,11)(13,14,15,16)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11720898, #11720899, #11720900, …
maximal normal subgroup of	#11720898, #11720899, #11720900, …
maximal quotient of	Dic₃×C₉⋊C₈, #11720258, C₃⋊C₈×Dic₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 87);