Finite Group Databasebeta

← Prev (#27210516) Next (#27210518) →

C2×C13⋊C3×D85 #27210517

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

Aliases

direct productC2×C13⋊C3×D85
unambiguous semidirect product(C2×C5)⋊(D17×C13⋊C3)
unambiguous semidirect product(C2×C17)⋊(D5×C13⋊C3)
unambiguous semidirect product(C2×C13×D85)⋊C3

Splittings

Fitting, socleC2×C5×C13×C17 ⋊ C2×C3
derived, HallC5×C13×C17 ⋊ C22×C3
HallC2×C13×D85 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C22
HallC17×C13⋊C3 ⋊ C2×D5
HallC13×C17 ⋊ C2×C3×D5
HallC5×C13⋊C3 ⋊ C2×D17
HallC5×C17 ⋊ C22×C13⋊C3
HallC5×C13 ⋊ C2×C3×D17
SylowC17 ⋊ C2×D5×C13⋊C3
SylowC13 ⋊ C2×C3×D85
SylowC5 ⋊ C2×D17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×D85
commutator, cosocle, hypocenterC5×C13×C17C22×C3
FrattiniC1G
Fitting, socleC2×C5×C13×C17C2×C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 2210

A minimal faithful permutation representation — 2 generators on 37 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20)(21,22)(24,25,27)(26,29,32)(28,31,30)(33,35,34);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,21,22,20)(23,24,26,25,28,32,29,33,35,27,30,34,31)(36,37)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 67);