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C22⋊(C13⋊C3)×C29⋊C7 #44539797

order31668
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22⋊(C13⋊C3)×C29⋊C7
unambiguous semidirect productC22⋊(C13⋊C3×C29⋊C7)
unambiguous semidirect productC13⋊(A4×C29⋊C7)
unambiguous semidirect productC29⋊(C7×C22⋊(C13⋊C3))
unambiguous semidirect product(C22×C29⋊C7)⋊(C13⋊C3)
unambiguous semidirect product(C13×C29⋊C7)⋊A4
unambiguous semidirect product(C29×C22⋊(C13⋊C3))⋊C7

Splittings

Fitting, socle, derived, HallC22×C13×C29 ⋊ C3×C7
HallC22×C13×C29⋊C7 ⋊ C3
HallC29×C22⋊(C13⋊C3) ⋊ C7
HallC13×C29⋊C7 ⋊ A4
HallC22×C29⋊C7 ⋊ C13⋊C3
HallC13×C29 ⋊ C7×A4
HallC22×C29 ⋊ C7×C13⋊C3
HallC22×C13 ⋊ C3×C29⋊C7
SylowC29 ⋊ C7×C22⋊(C13⋊C3)
SylowC13 ⋊ A4×C29⋊C7
SylowC22 ⋊ C13⋊C3×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C13×C29C3×C7
LCSG ▷ C22×C13×C29
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1508

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 92);