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C5×D39⋊D17 #27210564

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

Aliases

direct productC5×D39⋊D17
unambiguous semidirect productD39⋊(C5×D17)
unambiguous semidirect productD51⋊(C5×D13)
unambiguous semidirect productD221⋊(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 ⋊ D3×D13
HallC5×C13 ⋊ D3×D17
HallC3×C17 ⋊ C2×C5×D13
HallC3×C13 ⋊ C2×C5×D17
SylowC17 ⋊ C5×D3×D13
HallC3×C5 ⋊ D13×D17
SylowC13 ⋊ C5×D3×D17
SylowC3 ⋊ C5×D13×D17

Subgroups

subgroupG/H
center, hypercenterC5D39⋊D17
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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 114);