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C₅₃×Dic₁₃⋊C₉ #37613583

order	24804
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₅₃)
unambiguous semidirect product	(Dic₁₃×C₅₃)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₅₃
Hall	C₅₃×C₁₃⋊C₉ ⋊ C₄
Hall	Dic₁₃×C₅₃ ⋊ C₉
Hall	C₁₃×C₅₃ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₅₃
Hall	Dic₁₃ ⋊ C₉×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₅₃
Frattini	C₂×C₃	C₅₃×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₅₃	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₅₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₅₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24804

Conjugacy classes & character table

2544 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 15);