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C₄×D₃×C₁₁ #63151

order	264
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂³×C₅×D₃ (order 240) · Inn(G) = D₃ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₃×C₁₁

Splittings

Fitting	C₃×C₄×C₁₁ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄×C₁₁
Hall	C₃×C₁₁ ⋊ C₂×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₁₁	D₃
commutator, hypocenter	C₃	C₂×C₄×C₁₁
Frattini	C₂	C₂×D₃×C₁₁
Fitting	C₃×C₄×C₁₁	C₂
socle	C₂×C₃×C₁₁	C₂²
prime radical	C₂×D₃×C₁₁	C₂
cosocle	C₂×C₃	C₂²×C₁₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₄×C₁₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₁₁⋊C₈, #10587139, D₃×C₈×C₁₁, …
maximal normal subgroup of	D₃×C₁₁⋊C₈, #10587139, D₃×C₈×C₁₁, …
maximal quotient of	D₃×C₈×C₁₁, C₁₁×ΓL(1,𝔽₂₅), C₄×C₁₁×Dic₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 19);