Finite Group Databasebeta

← Prev (#27210559) Next (#27210561) →

C5×D17×D39 #27210560

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

Aliases

direct productC5×D17×D39
unambiguous semidirect product(C3×D17)⋊(C5×D13)
unambiguous semidirect product(C13×D17)⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C22
derived, HallC3×C13×C17 ⋊ C22×C5
HallC5×C13×C17 ⋊ C2×D3
HallC3×C5×C17 ⋊ C2×D13
HallC13×C17 ⋊ C2×C5×D3
HallC3×C5×C13 ⋊ C2×D17
HallC5×C17 ⋊ C2×D39
HallC5×C13 ⋊ D3×D17
HallC3×C17 ⋊ C2×C5×D13
HallC3×C13 ⋊ C2×C5×D17
SylowC17 ⋊ C2×C5×D39
HallC3×C5 ⋊ D13×D17
SylowC13 ⋊ C5×D3×D17
SylowC3 ⋊ C5×D13×D17

Subgroups

subgroupG/H
center, hypercenterC5D17×D39
commutator, cosocle, hypocenterC3×C13×C17C22×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C17C22
LCSG ▷ C3×C13×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 3315

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18,20,22,24,26,28,30,32,33,31,29,27,25,23,21,19)(34,35,36,37,38);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 110);