C₃×#64972 #11749580

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×#64972

Splittings

Hall	C₃×C₅ ⋊ #499
Sylow	C₅ ⋊ C₃×#499

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂³×C₃
Frattini	C₂×C₄	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×#499
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3)(4,5,7,8,6)(17,19,20,26,21,27,29,31)(18,23,24,25,22,30,28,32);(9,11,12,16)(10,13,14,15)(18,22)(23,30)(24,28)(25,32);(5,6)(7,8)(9,10,12,14)(11,15,16,13)(17,18,21,22)(19,25,27,32)(20,28,29,24)(23,31,30,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10598054, C₃×#10597959, #14278498, …
maximal normal subgroup of	C₃×#10598054, C₃×#10597959, #14278498, …
maximal quotient of	C₃×#10600559, C₃×#10600562, C₃×#10600563, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3775);

C3×#64972 #11749580