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C2×C3⋊(C13⋊(D41⋊C5)) #44544382

order31980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C13⋊(D41⋊C5))
unambiguous semidirect product(C2×C3)⋊(C13⋊(D41⋊C5))
unambiguous semidirect product(C2×C13)⋊(C3⋊(D41⋊C5))
unambiguous semidirect product(C2×C41⋊C5)⋊D39
unambiguous semidirect product(C2×D1599)⋊C5

Splittings

Fitting, socleC2×C3×C13×C41 ⋊ C2×C5
derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallC2×D1599 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×D3
HallC3×C41⋊C5 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC41⋊C5 ⋊ C2×D39
HallC3×C41 ⋊ C2×C5×D13
SylowC41 ⋊ C2×C5×D39
HallC3×C13 ⋊ C2×D41⋊C5
SylowC13 ⋊ C2×C3⋊(D41⋊C5)
SylowC3 ⋊ C2×C13⋊(D41⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C13⋊(D41⋊C5))
commutator, cosocle, hypocenterC3×C13×C41C22×C5
FrattiniC1G
Fitting, socleC2×C3×C13×C41C2×C5
LCSG ▷ C3×C13×C41
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 3198

A minimal faithful permutation representation — 2 generators on 59 points:

(4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(20,24,25,41,45,21,22,30,32,40)(23,37,38,43,44,27,28,52,31,54)(26,49,50,51,39,34,35,59,36,29)(33,56,57,42,55,47,48,58,46,53);(1,2)(3,4,5)(6,7,9,11,13,15,17,18,16,14,12,10,8)(19,20,23,29,40,52,55,59,54,43,22,26,36,49,57,56,32,46,25,33,28,37,47,30,42,41,48,58,35,51,34,24,31,44,50,53,38,45,39,27,21)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 110);