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C3×#65976 #11755653

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#65976

Splittings

FittingC3×C5×C22⋊Q8 ⋊ C2
HallC3×C5 ⋊ #552
SylowC5 ⋊ C3×#552

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C22⋊Q8C2
socleC22×C3×C5C24
prime radicalC2×C3×C22⋊D5C22
hypercenterC3×C22⋊Q8D5
hypocenterC5C3×#552
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊Q8

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10611890, C3×#10612506, #14458715, …
maximal normal subgroup ofC3×#10611890, C3×#10612506, #14458715, …
maximal quotient ofC3×#10606123, C3×#10605609, C3×#10607710, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9848);