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C5×D17×D13⋊C3 #27210481

order13260
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D17×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×D17)
unambiguous semidirect product(D13×D17)⋊(C3×C5)
unambiguous semidirect product(D17×C13⋊C3)⋊(C2×C5)
unambiguous semidirect product(C17×D13⋊C3)⋊(C2×C5)
unambiguous semidirect product(C17⋊(D13⋊C3))⋊(C2×C5)
unambiguous semidirect product(C5×D13×D17)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C22×C3
derived, HallC13×C17 ⋊ C22×C3×C5
HallC5×D13×D17 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C22
HallD13×D17 ⋊ C3×C5
HallC17×C13⋊C3 ⋊ C22×C5
HallC5×C13⋊C3 ⋊ C2×D17
HallC5×C17 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×C3×D17
HallC13⋊C3 ⋊ C2×C5×D17
SylowC17 ⋊ C2×C5×D13⋊C3
SylowC13 ⋊ C2×C3×C5×D17

Subgroups

subgroupG/H
center, hypercenterC5D17×D13⋊C3
commutator, cosocle, hypocenterC13×C17C22×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C17C22×C3
LCSG ▷ C13×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1105

A minimal faithful permutation representation — 2 generators on 35 points:

(2,6,7,3,4,8)(5,12,11,9,10,13)(14,15,17,19,21,23,25,27,29,30,28,26,24,22,20,18,16)(31,32,33,34,35);(1,2,5,4,8,11,10,12,13,7,6,9,3)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)

Conjugacy classes & character table

400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 31);