Finite Group Databasebeta

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C29×C3⋊D195 #46800277

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

Aliases

direct productC29×C3⋊D195
unambiguous semidirect productC3⋊(C29×D195)
unambiguous semidirect productC5⋊(C29×C3⋊D39)
unambiguous semidirect productC13⋊(C29×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C13×C29 ⋊ C2
derived, HallC32×C5×C13 ⋊ C2×C29
HallC32×C13×C29 ⋊ D5
HallC5×C13×C29 ⋊ C3⋊D3
HallC32×C5×C29 ⋊ D13
HallC13×C29 ⋊ C3⋊D15
HallC32×C29 ⋊ D65
HallC5×C29 ⋊ C3⋊D39
HallC32×C13 ⋊ D5×C29
HallC5×C13 ⋊ C3⋊D3×C29
HallC32×C5 ⋊ D13×C29
SylowC13 ⋊ C29×C3⋊D15
SylowC32 ⋊ C29×D65
SylowC5 ⋊ C29×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC29C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C2×C29
FrattiniC1G
Fitting, socleC32×C5×C13×C29C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

8526 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 63);