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C3×#65872 #11755549

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

Aliases

direct productC3×#65872

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #529
SylowC5 ⋊ C3×#529

Subgroups

subgroupG/H
centerC2×C3×C4C22×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
prime radicalC3×#4085C2
hypercenterC3×C4×D4D5
hypocenterC5C3×#529
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

468 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)(10,14)(11,15)(18,22)(21,24);(17,19,20,23)(18,21,22,24);(9,11)(10,13)(12,15)(14,16);(5,6)(7,8)(9,10,12,14)(11,13,15,16)(17,18,20,22)(19,21,23,24)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10611131, C3×#10611185, #14419173, …
maximal normal subgroup ofC3×#10611131, C3×#10611185, #14419173, …
maximal quotient ofC3×#10605168, C3×#10605169, C3×#10614049, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9744);