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C2×C3⋊(C13⋊(D29⋊C7)) #44539804

order31668
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C13⋊(D29⋊C7))
unambiguous semidirect product(C2×C3)⋊(C13⋊(D29⋊C7))
unambiguous semidirect product(C2×C13)⋊(C3⋊(D29⋊C7))
unambiguous semidirect product(C2×C29⋊C7)⋊D39
unambiguous semidirect product(C2×D1131)⋊C7

Splittings

Fitting, socleC2×C3×C13×C29 ⋊ C2×C7
derived, HallC3×C13×C29 ⋊ C22×C7
HallC3×C13×C29⋊C7 ⋊ C22
HallC2×D1131 ⋊ C7
HallC13×C29⋊C7 ⋊ C2×D3
HallC3×C29⋊C7 ⋊ C2×D13
HallC13×C29 ⋊ C2×D3×C7
HallC29⋊C7 ⋊ C2×D39
HallC3×C29 ⋊ C2×C7×D13
HallC3×C13 ⋊ C2×D29⋊C7
SylowC29 ⋊ C2×C7×D39
SylowC13 ⋊ C2×C3⋊(D29⋊C7)
SylowC3 ⋊ C2×C13⋊(D29⋊C7)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C13⋊(D29⋊C7))
commutator, cosocle, hypocenterC3×C13×C29C22×C7
FrattiniC1G
Fitting, socleC2×C3×C13×C29C2×C7
LCSG ▷ C3×C13×C29
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 2262

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 99);