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C₃²×#261 #90861

order	468
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

C₃²×#261

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	#261
commutator, hypocenter	C₁₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃	C₄
prime radical	C₃²×D₁₃	C₂
cosocle	D₁₃	C₂×C₃²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃²

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 117

A minimal faithful permutation representation — 2 generators on 19 points:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₃×#261, C₃⋊D₃×#261, C₂×C₃²×#261, …
maximal normal subgroup of	C₃×D₃×#261, C₃⋊D₃×#261, C₂×C₃²×#261, …
maximal quotient of	C₃²×#1057, C₂×C₃²×#261, C₃×C₉×#261, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 36);