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C3×#89166 #13050343

order1320
isoclinismisoclinic class of D5×D11
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#89166

Splittings

derived, HallC5×C11 ⋊ C2×C3×C4
HallC3×C5×C11 ⋊ C2×C4
HallC3×C11 ⋊ C4×D5
HallC3×C5 ⋊ C4×D11
SylowC11 ⋊ C3×C4×D5
SylowC5 ⋊ C3×C4×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×D11
commutator, hypocenterC5×C11C2×C3×C4
FrattiniC2C3×D5×D11
Fitting, socleC2×C3×C5×C11C22
prime radicalC2×C3×D55C2
cosocleC2×C5×C11C22×C3
LCSG ▷ 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)(20,22,23,21);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16,18,19,17)(20,21,23,22)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 47);