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D₃×Dic₁₂ #63799

order	288
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

D₃×Dic₁₂

Splittings

C₃² ⋊ C₂×Q₁₆

Subgroups

	subgroup	G/H
center	C₂	D₃×D₁₂
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂×D₃²
Fitting	C₃²×C₈	C₂²
socle	C₂×C₃²	C₂×D₄
prime radical	C₂×C₃×D₃	D₄
hypercenter	C₈	D₃²
hypocenter	C₃²	C₂×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

129 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 22 points:

(1,3,10,14,5,12,4,11)(2,6,13,16,8,15,7,9)(17,18,19)(20,21,22);(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(21,22);(18,19)

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#800, D₃×Dic₂₄, #10590238, …
maximal normal subgroup of	D₃×#800, D₃×Dic₂₄, #10590238, …
maximal quotient of	D₃×#816, D₃×#818, #10590682, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 447);