Finite Group Databasebeta

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C3×D13×D29⋊C7 #44539783

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

Aliases

direct productC3×D13×D29⋊C7
unambiguous semidirect productD29⋊(C3×C7×D13)
unambiguous semidirect product(C3×D13×D29)⋊C7

Splittings

Fitting, socle, HallC3×C13×C29 ⋊ C22×C7
derived, HallC13×C29 ⋊ C22×C3×C7
HallC3×C13×C29⋊C7 ⋊ C22
HallC3×D13×D29 ⋊ C7
HallC13×C29⋊C7 ⋊ C22×C3
HallD13×D29 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ C2×D13
HallC29⋊C7 ⋊ C2×C3×D13
HallC3×C29 ⋊ C2×C7×D13
HallC3×C13 ⋊ C2×D29⋊C7
SylowC29 ⋊ C2×C3×C7×D13
SylowC13 ⋊ C2×C3×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3D13×D29⋊C7
commutator, cosocle, hypocenterC13×C29C22×C3×C7
FrattiniC1G
Fitting, socleC3×C13×C29C22×C7
LCSG ▷ C13×C29
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 78);