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D17×C5⋊(D13⋊C3) #27210504

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

Aliases

direct productD17×C5⋊(D13⋊C3)
unambiguous semidirect product(C5×D17)⋊(D13⋊C3)
unambiguous semidirect product(D17×C13⋊C3)⋊D5
unambiguous semidirect product(D17×D65)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C17 ⋊ C22×C3
HallD17×D65 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C22
HallC17×C13⋊C3 ⋊ C2×D5
HallC13×C17 ⋊ C2×C3×D5
HallC5×C13⋊C3 ⋊ C2×D17
HallC5×C17 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×C3×D17
HallC13⋊C3 ⋊ D5×D17
SylowC17 ⋊ C2×C5⋊(D13⋊C3)
SylowC13 ⋊ C3×D5×D17
SylowC5 ⋊ D17×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C17C22×C3
LCSG ▷ C5×C13×C17
UCSC1

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

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 54);