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C13⋊C3×C22⋊D5 #13095600

order1560
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC13⋊C3×C22⋊D5
unambiguous semidirect product(C13×C22⋊D5)⋊C3

Splittings

FittingC22×C5×C13 ⋊ C2×C3
HallC13×C22⋊D5 ⋊ C3
HallC5×C13⋊C3 ⋊ D4
HallC5×C13 ⋊ C3×D4
SylowC13 ⋊ C3×C22⋊D5
SylowC5 ⋊ D4×C13⋊C3

Subgroups

subgroupG/H
center, FrattiniC2C2×D5×C13⋊C3
commutator, socle, cosocleC2×C5×C13C22×C3
FittingC22×C5×C13C2×C3
hypercenterC22D5×C13⋊C3
hypocenterC5×C13C3×D4
LCSG ▷ C2×C5×C13 ▷ C5×C13
UCSC1 ◁ C2 ◁ C22

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 260

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 36);