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C₂×C₂₅×C₃₁⋊C₉ #28358368

order	13950
isoclinism	isoclinic class of C₃₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₅×C₃₁⋊C₉
unambiguous semidirect product	(C₂×C₂₅×C₃₁)⋊C₉

Splittings

derived, Sylow	C₃₁ ⋊ C₂×C₉×C₂₅
Hall	C₂×C₂₅×C₃₁ ⋊ C₉
Hall	C₂₅×C₃₁ ⋊ C₂×C₉
Hall	C₂×C₃₁ ⋊ C₉×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₅	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₂×C₉×C₂₅
Frattini	C₃×C₅	C₂×C₅×C₃₁⋊C₃
Fitting	C₂×C₃×C₂₅×C₃₁	C₃
socle, prime radical	C₂×C₃×C₅×C₃₁	C₃×C₅
cosocle	C₃×C₅×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₅×Dic₃₁⋊C₉, Dic₂₅×C₃₁⋊C₉, (C₃₁⋊C₉)⋊Dic₂₅, …
maximal normal subgroup of	C₂₅×Dic₃₁⋊C₉, Dic₂₅×C₃₁⋊C₉, (C₃₁⋊C₉)⋊Dic₂₅, …
maximal quotient of	C₄×C₂₅×C₃₁⋊C₉, C₂²×C₂₅×C₃₁⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 11);