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C3×#66061 #11755738

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#66061

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ D4×Q8
SylowC5 ⋊ C3×D4×Q8

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×D4×Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10601998, C3×#10599250, #14289238, …
maximal normal subgroup ofC3×#10601998, C3×#10599250, #14289238, …
maximal quotient ofC3×#10608345, C3×#10606091, C3×#10607933, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9933);