Finite Group Databasebeta

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C2×C3×C5×C29×C13⋊C3 #46800255

order33930
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C29 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C29×C13⋊C3
unambiguous semidirect product(C2×C13)⋊(C32×C5×C29)
unambiguous semidirect product(C2×C3×C13)⋊(C3×C5×C29)
unambiguous semidirect product(C2×C5×C13)⋊(C32×C29)
unambiguous semidirect product(C2×C3×C5×C13)⋊(C3×C29)
unambiguous semidirect product(C2×C13×C29)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C13×C29)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×C29)⋊C32
unambiguous semidirect product(C2×C3×C5×C13×C29)⋊C3

Splittings

Fitting, socleC2×C3×C5×C13×C29 ⋊ C3
derived, SylowC13 ⋊ C2×C32×C5×C29
HallC2×C5×C13×C29 ⋊ C32
HallC5×C13×C29 ⋊ C2×C32
HallC2×C13×C29 ⋊ C32×C5
HallC13×C29 ⋊ C2×C32×C5
HallC2×C5×C13 ⋊ C32×C29
HallC5×C13 ⋊ C2×C32×C29
HallC2×C13 ⋊ C32×C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C29C13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C5×C29
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C29C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11310

Conjugacy classes & character table

6090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 41);