Finite Group Databasebeta

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C29×C5⋊(D31⋊C3) #41004212

order26970
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C5⋊(D31⋊C3)
unambiguous semidirect productC5⋊(C29×D31⋊C3)
unambiguous semidirect product(C31⋊C3)⋊(D5×C29)
unambiguous semidirect productD155⋊(C3×C29)
unambiguous semidirect product(C29×D155)⋊C3

Splittings

Fitting, socle, HallC5×C29×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C3×C29
HallC5×C29×C31⋊C3 ⋊ C2
HallC29×D155 ⋊ C3
HallC29×C31⋊C3 ⋊ D5
HallC29×C31 ⋊ C3×D5
HallC5×C31⋊C3 ⋊ C2×C29
HallD155 ⋊ C3×C29
HallC5×C29 ⋊ D31⋊C3
HallC31⋊C3 ⋊ D5×C29
SylowC31 ⋊ C3×D5×C29
SylowC5 ⋊ C29×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC29C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C3×C29
FrattiniC1G
Fitting, socleC5×C29×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4495

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 31);