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C₂³×C₁₃⋊C₉ #11745472

order	936
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₁₃⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂³×C₉
Hall	C₂³×C₁₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂³×C₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂³×C₉
Frattini	C₃	C₂³×C₁₃⋊C₃
Fitting, socle, prime radical	C₂³×C₃×C₁₃	C₃
cosocle	C₃×C₁₃	C₂³×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³×C₃

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 936

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2)(8,9,11)(10,13,16)(12,15,14)(17,19,18)(20,21,23,22,24,26,25,27,28);(3,4)(7,8,10,9,12,16,13,17,19,11,14,18,15);(5,6)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(936, 65);