C₃×#65226 #11749834

order	960
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃×#65226

Splittings

Hall	C₃×C₅ ⋊ #383
Sylow	C₅ ⋊ C₃×#383

Subgroups

	subgroup	G/H
center	C₂³×C₃	C₂²×D₅
commutator	C₂²×C₅	C₂²×C₃×C₄
Frattini	C₂³	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂
socle, prime radical	C₂³×C₃×C₅	C₂³
cosocle	C₂³×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄²	D₅
hypocenter	C₅	C₃×#383
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄²

276 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)(14,18)(17,20)(21,23,24,28)(22,26,25,27);(13,15,16,19)(14,17,18,20)(22,25)(26,27);(5,6)(7,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20)(21,22)(23,27)(24,25)(26,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10598157, C₃×#10598243, #14277025, …
maximal normal subgroup of	C₃×#10598157, C₃×#10598243, #14277025, …
maximal quotient of	C₃×#10602327, C₃×#10600209, C₃×#10600186, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4029);

C3×#65226 #11749834