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C5×D3×C17×D13 #27210561

order13260
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×C17×D13
unambiguous semidirect product(D3×C13)⋊(C2×C5×C17)
unambiguous semidirect product(C3×D13)⋊(C2×C5×C17)
unambiguous semidirect productD39⋊(C2×C5×C17)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C17D3×D13
commutator, cosocle, hypocenterC3×C13C22×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C22
LCSG ▷ C3×C13
UCSC1 ◁ C5×C17

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

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 111);