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C₂×C₂₃×C₅²⋊C₉ #23780353

order	10350
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂×C₂₃×C₅²⋊C₉
unambiguous semidirect product	(C₂×C₅²)⋊(C₉×C₂₃)
unambiguous semidirect product	(C₂×C₅²×C₂₃)⋊C₉

Splittings

derived, Sylow	C₅² ⋊ C₂×C₉×C₂₃
Hall	C₂×C₅²×C₂₃ ⋊ C₉
Hall	C₅²×C₂₃ ⋊ C₂×C₉
Hall	C₂×C₅² ⋊ C₉×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₃	C₅²⋊C₃
commutator, hypocenter	C₅²	C₂×C₉×C₂₃
Frattini	C₃	C₂×C₂₃×C₅²⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₅²×C₂₃	C₃
cosocle	C₃×C₅²	C₂×C₃×C₂₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₂₃

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#11744607, C₂₃⋊#11744607, C₂₃×#1039⋊C₉, …
maximal normal subgroup of	C₂₃×#11744607, C₂₃⋊#11744607, C₂₃×#1039⋊C₉, …
maximal quotient of	C₄×C₂₃×C₅²⋊C₉, C₂²×C₂₃×C₅²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 27);