Finite Group Databasebeta

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D₉×C₂₃×C₂₅ #23780331

order	10350
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₂₃×C₂₅
unambiguous semidirect product	C₉⋊(C₂×C₂₃×C₂₅)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃×C₂₅	D₉
commutator, hypocenter	C₉	C₂×C₂₃×C₂₅
Frattini	C₃×C₅	C₅×D₃×C₂₃
Fitting	C₉×C₂₃×C₂₅	C₂
socle	C₃×C₅×C₂₃	C₅×D₃
prime radical	C₅×D₉×C₂₃	C₅
cosocle	C₅×C₉	C₂×C₅×C₂₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂₃×C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₂₅×D₂₃, D₉×C₂₃×D₂₅, D₉×D₅₇₅, …
maximal normal subgroup of	D₉×C₂₅×D₂₃, D₉×C₂₃×D₂₅, D₉×D₅₇₅, …
maximal quotient of	C₂₃×C₂₅×Dic₉, C₂×D₉×C₂₃×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 5);