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D13⋊C3×D85 #27210506

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

Aliases

direct productD13⋊C3×D85
unambiguous semidirect productD13⋊(C3×D85)
unambiguous semidirect product(C5×D13⋊C3)⋊D17
unambiguous semidirect product(C17×D13⋊C3)⋊D5
unambiguous semidirect product(D13×D85)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C17 ⋊ C22×C3
HallD13×D85 ⋊ 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 ⋊ C2×D85
SylowC17 ⋊ D5×D13⋊C3
SylowC13 ⋊ C2×C3×D85
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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 56);