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C₃²×Dic₁₃ #90848

order	468
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

C₃²×Dic₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₃
commutator, hypocenter	C₁₃	C₃²×C₄
Frattini	C₂	C₃²×D₁₃
Fitting, socle, prime radical	C₂×C₃²×C₁₃	C₂
cosocle	C₂×C₁₃	C₂×C₃²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃²

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 — 2 generators on 23 points:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃²×#1057, C₃×C₃⋊#1057, C₃⋊(C₃⋊#1057), …
maximal normal subgroup of	C₃²×#1057, C₃×C₃⋊#1057, C₃⋊(C₃⋊#1057), …
maximal quotient of	C₃²×#1055, C₂×C₃²×Dic₁₃, C₃×C₉×Dic₁₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 23);