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C₂×C₉×C₃₁⋊C₂₅ #28358367

order	13950
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉	ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃₁	C₂×C₉×C₂₅
Frattini	C₃×C₅	C₂×C₃×ΓL(1,𝔽₃₂)
Fitting	C₂×C₅×C₉×C₃₁	C₅
socle, prime radical	C₂×C₃×C₅×C₃₁	C₃×C₅
cosocle	C₃×C₅×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

990 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×Dic₃₁⋊C₂₅, Dic₉×C₃₁⋊C₂₅, C₉⋊(Dic₃₁⋊C₂₅), …
maximal normal subgroup of	C₉×Dic₃₁⋊C₂₅, Dic₉×C₃₁⋊C₂₅, C₉⋊(Dic₃₁⋊C₂₅), …
maximal quotient of	C₄×C₉×C₃₁⋊C₂₅, C₂²×C₉×C₃₁⋊C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 10);