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C5×C17×C22⋊(C13⋊C3) #27210609

order13260
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC5×C17×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C5×C17×C13⋊C3)
unambiguous semidirect productC13⋊(C5×A4×C17)
unambiguous semidirect product(C22×C5)⋊(C17×C13⋊C3)
unambiguous semidirect product(C5×C13)⋊(A4×C17)
unambiguous semidirect product(C22×C17)⋊(C5×C13⋊C3)
unambiguous semidirect product(C13×C17)⋊(C5×A4)
unambiguous semidirect product(C22×C5×C17)⋊(C13⋊C3)
unambiguous semidirect product(C5×C13×C17)⋊A4

Splittings

Fitting, socle, HallC22×C5×C13×C17 ⋊ C3
derived, HallC22×C13 ⋊ C3×C5×C17
HallC5×C13×C17 ⋊ A4
HallC22×C13×C17 ⋊ C3×C5
HallC22×C5×C17 ⋊ C13⋊C3
HallC22×C5×C13 ⋊ C3×C17
HallC13×C17 ⋊ C5×A4
HallC22×C17 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ A4×C17
HallC22×C5 ⋊ C17×C13⋊C3
SylowC13 ⋊ C5×A4×C17
SylowC22 ⋊ C5×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C17C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C5×C17
FrattiniC1G
Fitting, socleC22×C5×C13×C17C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 4420

A minimal faithful permutation representation — 2 generators on 39 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)(35,36,37,38,39);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,17)(15,16)

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 159);