Finite Group Databasebeta

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C4×C13⋊C3×C29⋊C7 #44539712

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

Aliases

direct productC4×C13⋊C3×C29⋊C7
unambiguous semidirect product(C4×C13)⋊(C3×C29⋊C7)
unambiguous semidirect product(C4×C29)⋊(C7×C13⋊C3)
unambiguous semidirect product(C4×C29×C13⋊C3)⋊C7
unambiguous semidirect product(C4×C13×C29⋊C7)⋊C3

Splittings

Fitting, HallC4×C13×C29 ⋊ C3×C7
derived, HallC13×C29 ⋊ C3×C4×C7
HallC4×C13×C29⋊C7 ⋊ C3
HallC4×C29×C13⋊C3 ⋊ C7
HallC13×C29⋊C7 ⋊ C3×C4
HallC29×C13⋊C3 ⋊ C4×C7
HallC4×C29 ⋊ C7×C13⋊C3
HallC4×C13 ⋊ C3×C29⋊C7
SylowC29 ⋊ C4×C7×C13⋊C3
SylowC13 ⋊ C3×C4×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC4C13⋊C3×C29⋊C7
commutator, hypocenterC13×C29C3×C4×C7
FrattiniC2C2×C13⋊C3×C29⋊C7
FittingC4×C13×C29C3×C7
socle, cosocleC2×C13×C29C2×C3×C7
prime radicalC2×C13⋊C3×C29⋊C7C2
LCSG ▷ C13×C29
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1508

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 7);