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C3×#89167 #13050344

order1320
isoclinismisoclinic class of #89167
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#89167

Splittings

HallC3×C5×C11 ⋊ D4
HallC5×C11 ⋊ C3×D4
HallC3×C11 ⋊ C22⋊D5
HallC3×C5 ⋊ C22⋊D11
SylowC11 ⋊ C3×C22⋊D5
SylowC5 ⋊ C3×C22⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×D11
commutator, cosocleC2×C5×C11C22×C3
FrattiniC2C3×D5×D11
Fitting, socleC2×C3×C5×C11C22
hypocenterC5×C11C3×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2×C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 660

A minimal faithful permutation representation — 2 generators on 23 points:

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 48);