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C₅₃×(C₅⋊D₅)⋊C₉ #37558695

order	23850
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₅₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅₃×(C₅⋊D₅)⋊C₉
unambiguous semidirect product	(C₅⋊D₅)⋊(C₉×C₅₃)
unambiguous semidirect product	(C₅⋊D₅×C₅₃)⋊C₉

Splittings

derived, Sylow	C₅² ⋊ C₂×C₉×C₅₃
Hall	C₅₃×C₅²⋊C₉ ⋊ C₂
Hall	C₅⋊D₅×C₅₃ ⋊ C₉
Hall	C₅²×C₅₃ ⋊ C₂×C₉
Hall	C₅²⋊C₉ ⋊ C₂×C₅₃
Hall	C₅⋊D₅ ⋊ C₉×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅₃	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₂×C₉×C₅₃
Frattini	C₃	C₅₃×(C₅⋊D₅)⋊C₃
Fitting, socle	C₃×C₅²×C₅₃	C₂×C₃
prime radical	C₃×C₅⋊D₅×C₅₃	C₃
cosocle	C₃×C₅²	C₂×C₃×C₅₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₅₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2385

Conjugacy classes & character table

1590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23850, 24);