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C₂₃×C₅²⋊C₉ #19104366

order	5175
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₂₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂₃×C₅²⋊C₉
unambiguous semidirect product	C₅²⋊(C₉×C₂₃)
unambiguous semidirect product	(C₅²×C₂₃)⋊C₉

Splittings

derived, Sylow	C₅² ⋊ C₉×C₂₃
Hall	C₅²×C₂₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₃	C₅²⋊C₃
commutator, hypocenter	C₅²	C₉×C₂₃
Frattini	C₃	C₂₃×C₅²⋊C₃
Fitting, socle	C₃×C₅²×C₂₃	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₂₃

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

759 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₂₃⋊#11744607, #90646⋊D₂₃, ((C₅⋊D₅)⋊C₉)⋊D₂₃, …
maximal subgroup of	C₂₃×C₂²⋊(C₅²⋊C₉), C₂₃×C₇⋊(C₅²⋊C₉), C₇×C₂₃×C₅²⋊C₉
maximal normal subgroup of	C₇×C₂₃×C₅²⋊C₉
maximal quotient of	C₂₃×C₂²⋊(C₅²⋊C₉), C₂₃×C₇⋊(C₅²⋊C₉), C₇×C₂₃×C₅²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5175, 4);