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C2×C7×C29⋊(D13⋊C3) #44539884

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

Aliases

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

Splittings

Fitting, socleC2×C7×C13×C29 ⋊ C2×C3
derived, HallC13×C29 ⋊ C22×C3×C7
HallC2×C7×D377 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C22
HallC7×C13×C29 ⋊ C22×C3
HallC2×D377 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D29
HallC7×C29 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D29
HallC13⋊C3 ⋊ C2×C7×D29
SylowC29 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D29

Subgroups

subgroupG/H
center, hypercenterC2×C7C29⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C29C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C13×C29C2×C3
LCSG ▷ C13×C29
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5278

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 179);