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C3×#66069 #11755746

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

Aliases

direct productC3×#66069

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ #563
SylowC5 ⋊ C3×#563

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C4⋊Q8C2
socleC22×C3×C5C24
prime radicalC2×C3×D20C22
hypercenterC3×C4⋊Q8D5
hypocenterC5C3×#563
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,14,13,15)(18,24)(22,30)(23,32)(29,31);(10,13)(14,15)(17,20,21,28)(18,23,24,32)(19,25,26,27)(22,29,30,31);(11,16)(14,15)(17,19,21,26)(18,22,24,30)(20,27,28,25)(23,31,32,29);(5,6)(7,8)(9,10)(11,15)(12,13)(14,16)(17,18)(19,22)(20,23)(21,24)(25,29)(26,30)(27,31)(28,32)

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10601786, C3×#10599960, #14316947, …
maximal normal subgroup ofC3×#10601786, C3×#10599960, #14316947, …
maximal quotient ofC3×#10607938, C3×#10608348, C3×#10607723, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9941);