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C₉×D₅₇₅ #23780330

order	10350
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅₇₅
unambiguous semidirect product	C₂₃⋊(C₉×D₂₅)
unambiguous semidirect product	C₂₅⋊(C₉×D₂₃)

Splittings

Fitting, Hall	C₉×C₂₃×C₂₅ ⋊ C₂
derived, Hall	C₂₃×C₂₅ ⋊ C₂×C₉
Hall	C₉×C₂₅ ⋊ D₂₃
Hall	C₉×C₂₃ ⋊ D₂₅
Sylow	C₂₅ ⋊ C₉×D₂₃
Sylow	C₂₃ ⋊ C₉×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₇₅
commutator, hypocenter	C₂₃×C₂₅	C₂×C₉
Frattini	C₃×C₅	C₃×D₁₁₅
Fitting	C₉×C₂₃×C₂₅	C₂
socle	C₃×C₅×C₂₃	C₃×D₅
prime radical	C₃×D₅₇₅	C₃
cosocle	C₃×C₂₃×C₂₅	C₂×C₃
LCS	G ▷ C₂₃×C₂₅
UCS	C₁ ◁ C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2601 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×D₂₅, D₉×D₅₇₅, D₂₀₇⋊D₂₅, …
maximal normal subgroup of	C₉×D₂₃×D₂₅, D₉×D₅₇₅, D₂₀₇⋊D₂₅, …
maximal quotient of	C₉×Dic₅₇₅, C₂×C₉×D₅₇₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 4);