C₃×#64988 #11749596

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃×#64988

Splittings

Hall	C₃×C₅ ⋊ #494
Sylow	C₅ ⋊ C₃×#494

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×#494
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈

244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10598063, #14278405, C₃×#10597965, …
maximal normal subgroup of	C₃×#10598063, #14278405, C₃×#10597965, …
maximal quotient of	C₃×#10598856, C₃×#10598857, C₃×#10598858, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3791);

C3×#64988 #11749596