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C₁₃×D₂₄ #10597643

order	624
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

C₁₃×D₂₄

Splittings

Fitting	C₃×C₈×C₁₃ ⋊ C₂
Hall	C₃×C₁₃ ⋊ D₈
Sylow	C₃ ⋊ C₁₃×D₈

Subgroups

	subgroup	G/H
center	C₂×C₁₃	D₁₂
commutator, cosocle	C₃×C₄	C₂²×C₁₃
Frattini	C₄	C₂×D₃×C₁₃
Fitting	C₃×C₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	D₄
hypercenter	C₈×C₁₃	D₃
hypocenter	C₃	C₁₃×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₈×C₁₃

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 312

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11927945, #11927947, #11927949, …
maximal normal subgroup of	#11927945, #11927947, #11927949, …
maximal quotient of	C₁₃×#800, C₁₃×D₄₈, C₁₃×Dic₂₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(624, 80);