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C2×(C13⋊C3)⋊(D29⋊C7) #44539774

order31668
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C13⋊C3)⋊(D29⋊C7)
unambiguous semidirect product(C2×C13⋊C3)⋊(D29⋊C7)
unambiguous semidirect product(C2×C29⋊C7)⋊(D13⋊C3)
unambiguous semidirect product(C2×C29⋊(D13⋊C3))⋊C7
unambiguous semidirect product(C2×C13⋊(D29⋊C7))⋊C3

Splittings

Fitting, socleC2×C13×C29 ⋊ C2×C3×C7
derived, HallC13×C29 ⋊ C22×C3×C7
HallC2×C13⋊(D29⋊C7) ⋊ C3
HallC13⋊C3×C29⋊C7 ⋊ C22
HallC2×C29⋊(D13⋊C3) ⋊ C7
HallC13×C29⋊C7 ⋊ C22×C3
HallC2×D377 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC29⋊C7 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×D29⋊C7
SylowC29 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2(C13⋊C3)⋊(D29⋊C7)
commutator, cosocle, hypocenterC13×C29C22×C3×C7
FrattiniC1G
Fitting, socleC2×C13×C29C2×C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 754

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 69);