Finite Group Databasebeta

← Prev (#44569150) Next (#44569152) →

C2×C5×C13⋊C3×C83 #44569151

order32370
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C83 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13⋊C3×C83
unambiguous semidirect product(C2×C13)⋊(C3×C5×C83)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C83)
unambiguous semidirect product(C2×C13×C83)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×C83)⋊C3

Splittings

Fitting, socle, HallC2×C5×C13×C83 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C83
HallC5×C13×C83 ⋊ C2×C3
HallC2×C13×C83 ⋊ C3×C5
HallC13×C83 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C83
HallC5×C13 ⋊ C2×C3×C83
HallC2×C13 ⋊ C3×C5×C83

Subgroups

subgroupG/H
center, hypercenterC2×C5×C83C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C83
FrattiniC1G
Fitting, socleC2×C5×C13×C83C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10790

Conjugacy classes & character table

5810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 2);