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C₅×D₃×#137 #11756161

order	960
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

C₅×D₃×#137

Splittings

Fitting	C₃×C₅×#137 ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×#137
Sylow	C₃ ⋊ C₂×C₅×#137

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#137	C₂
socle	C₂×C₃×C₅	C₂²×D₄
prime radical	C₅×D₃×#41	C₂
hypercenter	C₅×#137	D₃
hypocenter	C₃	C₂×C₅×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#137

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 240

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#455, D₃×#65491, C₅×D₃×#456, …
maximal normal subgroup of	C₅×D₃×#455, D₃×#65491, C₅×D₃×#456, …
maximal quotient of	C₅×D₃×#419, C₅×D₃×#417, C₅×D₃×#428, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10356);