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C₃×C₁₃⋊C₉ #66850

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

Aliases

direct product	C₃×C₁₃⋊C₉
unambiguous semidirect product	(C₃×C₁₃)⋊C₉

Splittings

C₁₃ ⋊ C₃×C₉

Subgroups

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

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 351

A minimal faithful permutation representation — 2 generators on 25 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(17,18,20,19,21,23,22,24,25);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,15,16)

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₁₃⋊C₉, D₃×C₁₃⋊C₉, C₃⋊(D₁₃⋊C₉), …
maximal normal subgroup of	C₃×D₁₃⋊C₉, D₃×C₁₃⋊C₉, C₃⋊(D₁₃⋊C₉), …
maximal quotient of	C₂×C₃×C₁₃⋊C₉, C₉×C₁₃⋊C₉, C₃²⋊(C₁₃⋊C₉), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(351, 6);