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C₃×#4313 #10587162

order	528
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₃×C₈×C₁₁ ⋊ C₂
Hall	C₃×C₁₁ ⋊ M₁₆
Sylow	C₁₁ ⋊ C₃×M₁₆

Subgroups

	subgroup	G/H
center	C₃×C₄	C₂×D₁₁
commutator	C₂×C₁₁	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×D₁₁
Fitting	C₃×C₈×C₁₁	C₂
socle	C₂×C₃×C₁₁	C₂×C₄
prime radical	C₂×C₃×D₁₁	C₄
cosocle	C₄×C₁₁	C₂²×C₃
hypercenter	C₃×C₈	D₁₁
hypocenter	C₁₁	C₃×M₁₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₃×C₄ ◁ C₃×C₈

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#4313, #11760696, #11760699, …
maximal normal subgroup of	D₃×#4313, #11760696, #11760699, …
maximal quotient of	C₃×Dic₁₁⋊C₈, C₃×#66879, C₃×(C₂×D₁₁)⋊C₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 32);