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C₂²×C₁₃⋊C₉ #90837

order	468
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₃⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂²×C₉
Hall	C₂²×C₁₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₉
Frattini	C₃	C₂²×C₁₃⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₁₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 468

A minimal faithful permutation representation — 2 generators on 26 points:

(3,4)(5,9,13,7,12,8,10,6,11)(15,16,18)(17,20,23)(19,22,21)(24,26,25);(1,2)(14,15,17,16,19,23,20,24,26,18,21,25,22)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×Dic₁₃⋊C₉, (C₂²⋊D₁₃)⋊C₉, C₂×C₄×C₁₃⋊C₉, …
maximal normal subgroup of	C₂×Dic₁₃⋊C₉, (C₂²⋊D₁₃)⋊C₉, C₂×C₄×C₁₃⋊C₉, …
maximal quotient of	C₂×C₄×C₁₃⋊C₉, D₄×C₁₃⋊C₉, Q₈×C₁₃⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 12);