Finite Group Databasebeta

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C5×C29×D13⋊C9 #46800233

order33930
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×D13⋊C9
unambiguous semidirect productD13⋊(C5×C9×C29)
unambiguous semidirect product(C13⋊C9)⋊(C2×C5×C29)
unambiguous semidirect product(C5×D13)⋊(C9×C29)
unambiguous semidirect product(D13×C29)⋊(C5×C9)
unambiguous semidirect product(C5×D13×C29)⋊C9

Splittings

derived, SylowC13 ⋊ C2×C5×C9×C29
HallC5×C29×C13⋊C9 ⋊ C2
HallC5×D13×C29 ⋊ C9
HallC29×C13⋊C9 ⋊ C2×C5
HallC5×C13×C29 ⋊ C2×C9
HallD13×C29 ⋊ C5×C9
HallC5×C13⋊C9 ⋊ C2×C29
HallC13×C29 ⋊ C2×C5×C9
HallC5×D13 ⋊ C9×C29
HallC13⋊C9 ⋊ C2×C5×C29
HallC5×C13 ⋊ C2×C9×C29
HallD13 ⋊ C5×C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C5×C29D13⋊C3
commutator, hypocenterC13C2×C5×C9×C29
FrattiniC3C5×C29×D13⋊C3
Fitting, socleC3×C5×C13×C29C2×C3
prime radicalC3×C5×D13×C29C3
cosocleC3×C13C2×C3×C5×C29
LCSG ▷ C13
UCSC1 ◁ C3×C5×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 19);