Finite Group Databasebeta

← Prev (#37527666) Next (#37527668) →

C59×C5⋊(D13⋊C3) #37527667

order23010
automorphism?
homologyAbelianization (H1) = C2×C3×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C59×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D5×C59)
unambiguous semidirect productD65⋊(C3×C59)
unambiguous semidirect product(C59×D65)⋊C3

Splittings

Fitting, socle, HallC5×C13×C59 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C59
HallC5×C13⋊C3×C59 ⋊ C2
HallC59×D65 ⋊ C3
HallC13⋊C3×C59 ⋊ D5
HallC13×C59 ⋊ C3×D5
HallC5×C59 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C2×C59
HallD65 ⋊ C3×C59
HallC13⋊C3 ⋊ D5×C59
SylowC13 ⋊ C3×D5×C59
SylowC5 ⋊ C59×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC59C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C2×C3×C59
FrattiniC1G
Fitting, socleC5×C13×C59C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3835

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 23);