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C₉×D₇₇₅ #28358371

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

Aliases

direct product	C₉×D₇₇₅
unambiguous semidirect product	C₂₅⋊(C₉×D₃₁)

Splittings

Fitting, Hall	C₉×C₂₅×C₃₁ ⋊ C₂
derived, Hall	C₂₅×C₃₁ ⋊ C₂×C₉
Hall	C₉×C₃₁ ⋊ D₂₅
Hall	C₉×C₂₅ ⋊ D₃₁
Sylow	C₃₁ ⋊ C₉×D₂₅
Sylow	C₂₅ ⋊ C₉×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇₇₅
commutator, hypocenter	C₂₅×C₃₁	C₂×C₉
Frattini	C₃×C₅	C₃×D₁₅₅
Fitting	C₉×C₂₅×C₃₁	C₂
socle	C₃×C₅×C₃₁	C₃×D₅
prime radical	C₃×D₇₇₅	C₃
cosocle	C₃×C₂₅×C₃₁	C₂×C₃
LCS	G ▷ C₂₅×C₃₁
UCS	C₁ ◁ C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3501 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₅×D₃₁, D₉×D₇₇₅, D₂₂₅⋊D₃₁, …
maximal normal subgroup of	C₉×D₂₅×D₃₁, D₉×D₇₇₅, D₂₂₅⋊D₃₁, …
maximal quotient of	C₉×Dic₇₇₅, C₂×C₉×D₇₇₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 14);