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C3×#65525 #11750133

order960
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#65525

Splittings

HallC3×C5 ⋊ #421
SylowC5 ⋊ C3×#421

Subgroups

subgroupG/H
centerC3×C4C2×C22⋊D5
commutatorC4×C5C22×C3×C4
FrattiniC2×C4C22×C3×D5
Fitting, prime radicalC2×C3×C5×#41C2
socleC2×C3×C5C2×C22⋊C4
cosocleC2×C4×C5C23×C3
hypercenterC2×C3×#41D5
hypocenterC5C3×#421
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10602939, C3×#10601088, #14297288, …
maximal normal subgroup ofC3×#10602939, C3×#10601088, #14297288, …
maximal quotient ofC3×#10602432, C3×#10602390, C3×#10602414, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4328);