Finite Group Databasebeta

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C3×C4×C13×C29⋊C7 #44539707

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C13×C29⋊C7
unambiguous semidirect product(C4×C29)⋊(C3×C7×C13)
unambiguous semidirect product(C3×C4×C29)⋊(C7×C13)
unambiguous semidirect product(C3×C4×C13×C29)⋊C7

Splittings

Fitting, HallC3×C4×C13×C29 ⋊ C7
derived, SylowC29 ⋊ C3×C4×C7×C13
HallC4×C13×C29 ⋊ C3×C7
HallC3×C13×C29 ⋊ C4×C7
HallC13×C29 ⋊ C3×C4×C7
HallC3×C4×C29 ⋊ C7×C13
HallC4×C29 ⋊ C3×C7×C13
HallC3×C29 ⋊ C4×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4×C13C29⋊C7
commutator, hypocenterC29C3×C4×C7×C13
FrattiniC2C2×C3×C13×C29⋊C7
FittingC3×C4×C13×C29C7
socleC2×C3×C13×C29C2×C7
prime radicalC2×C3×C13×C29⋊C7C2
cosocleC2×C29C2×C3×C7×C13
LCSG ▷ C29
UCSC1 ◁ C3×C4×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4524

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 2);