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C₁₁×C₁₉×C₁₃⋊C₉ #37587385

order	24453
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₁₉×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₉×C₁₁×C₁₉)
unambiguous semidirect product	(C₁₁×C₁₃)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₉×C₁₁×C₁₉
Hall	C₁₁×C₁₃×C₁₉ ⋊ C₉
Hall	C₁₃×C₁₉ ⋊ C₉×C₁₁
Hall	C₁₁×C₁₃ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₁₁×C₁₉
Frattini	C₃	C₁₁×C₁₉×C₁₃⋊C₃
Fitting, socle, prime radical	C₃×C₁₁×C₁₃×C₁₉	C₃
cosocle	C₃×C₁₃	C₃×C₁₁×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₁×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24453

Conjugacy classes & character table

4389 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24453, 3);