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C2×D5×C17×C13⋊C3 #27210516

order13260
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C17×C13⋊C3
unambiguous semidirect productC5⋊(C22×C17×C13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C2×C17×C13⋊C3)
unambiguous semidirect product(C2×D5×C13)⋊(C3×C17)
unambiguous semidirect product(C2×D5×C13×C17)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C17D5×C13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C3×C17
FrattiniC1G
Fitting, socleC2×C5×C13×C17C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C17

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 66);