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C₁₃×C₃⋊Dic₃ #90851

order	468
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₃×C₃⋊Dic₃
unambiguous semidirect product	C₃⋊(Dic₃×C₁₃)

Splittings

derived, Sylow	C₃² ⋊ C₄×C₁₃
Hall	C₃²×C₁₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₁₃
Frattini	C₂	C₁₃×C₃⋊D₃
Fitting, socle, prime radical	C₂×C₃²×C₁₃	C₂
cosocle	C₂×C₃²	C₂×C₁₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 468

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#14273043, #14273044, #14273045, …
maximal subgroup of	C₁₃×#622, #11745508, D₁₃×C₃⋊Dic₃, …
maximal normal subgroup of	C₁₃×#622, #11745508, D₁₃×C₃⋊Dic₃, …
maximal quotient of	C₁₃×C₃⋊(C₃⋊C₈), C₂×C₁₃×C₃⋊Dic₃, C₁₃×C₃⋊Dic₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 26);