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C3×#65110 #11749718

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

Aliases

direct productC3×#65110

Splittings

FittingC3×C5×#104 ⋊ C2
HallC3×C5 ⋊ #421
SylowC5 ⋊ C3×#421

Subgroups

subgroupG/H
centerC3×C4D4×D5
commutatorC4×C5C22×C3×C4
FrattiniC2×C4C22×C3×D5
FittingC3×C5×#104C2
socleC2×C3×C5C2×C22⋊C4
prime radicalC3×D5×#41C2
cosocleC2×C4×C5C23×C3
hypercenterC3×#104D5
hypocenterC5C3×#421
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#104

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#421, C2×C3×#65110, #14412857, …
maximal normal subgroup ofC3×D5×#421, C2×C3×#65110, #14412857, …
maximal quotient ofC3×#10598959, C3×#10599023, C3×#10598960, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3913);