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C₉×C₁₃⋊C₃ #66847

order	351
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

C₉×C₁₃⋊C₃

Splittings

Fitting	C₉×C₁₃ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₉
Frattini	C₃	C₃×C₁₃⋊C₃
Fitting	C₉×C₁₃	C₃
socle, cosocle	C₃×C₁₃	C₃²
prime radical	C₃×C₁₃⋊C₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₉

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 117

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

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×D₁₃⋊C₃, D₉×C₁₃⋊C₃, (C₁₃⋊C₃)⋊D₉, …
maximal normal subgroup of	C₉×D₁₃⋊C₃, D₉×C₁₃⋊C₃, (C₁₃⋊C₃)⋊D₉, …
maximal quotient of	C₂×C₉×C₁₃⋊C₃, C₉×C₁₃⋊C₉, (C₃×C₁₃⋊C₃)⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(351, 3);