Finite Group Databasebeta

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C₉×C₂₅×D₂₃ #23780328

order	10350
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₂₅×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂×C₉×C₂₅)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₅	D₂₃
commutator, hypocenter	C₂₃	C₂×C₉×C₂₅
Frattini	C₃×C₅	C₃×C₅×D₂₃
Fitting	C₉×C₂₃×C₂₅	C₂
socle, cosocle	C₃×C₅×C₂₃	C₂×C₃×C₅
prime radical	C₃×C₅×D₂₃	C₃×C₅
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₉×C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×D₂₅, D₉×C₂₅×D₂₃, D₂₃×D₂₂₅, …
maximal normal subgroup of	C₉×D₂₃×D₂₅, D₉×C₂₅×D₂₃, D₂₃×D₂₂₅, …
maximal quotient of	C₉×C₂₅×Dic₂₃, C₂×C₉×C₂₅×D₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 2);