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D5×C17×D13⋊C3 #27210505

order13260
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productD5×C17×D13⋊C3
unambiguous semidirect productD13⋊(C3×D5×C17)
unambiguous semidirect product(D5×D13)⋊(C3×C17)
unambiguous semidirect product(C5×D13⋊C3)⋊(C2×C17)
unambiguous semidirect product(D5×C13⋊C3)⋊(C2×C17)
unambiguous semidirect product(C5⋊(D13⋊C3))⋊(C2×C17)
unambiguous semidirect product(D5×C17×D13)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C22×C3
derived, HallC5×C13 ⋊ C22×C3×C17
HallD5×C17×D13 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C22
HallC17×C13⋊C3 ⋊ C2×D5
HallD5×D13 ⋊ C3×C17
HallC13×C17 ⋊ C2×C3×D5
HallC5×C13⋊C3 ⋊ C22×C17
HallC5×C17 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×D5×C17
SylowC13 ⋊ C2×C3×D5×C17
SylowC5 ⋊ C2×C17×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17D5×D13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C3×C17
FrattiniC1G
Fitting, socleC5×C13×C17C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C17

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 55);