Finite Group Databasebeta

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C5×D13⋊C3×C83 #44569168

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

Aliases

direct productC5×D13⋊C3×C83
unambiguous semidirect productD13⋊(C3×C5×C83)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C83)
unambiguous semidirect product(C5×D13)⋊(C3×C83)
unambiguous semidirect product(D13×C83)⋊(C3×C5)
unambiguous semidirect product(C5×D13×C83)⋊C3

Splittings

Fitting, socle, HallC5×C13×C83 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C83
HallC5×C13⋊C3×C83 ⋊ C2
HallC5×D13×C83 ⋊ C3
HallC13⋊C3×C83 ⋊ C2×C5
HallD13×C83 ⋊ C3×C5
HallC13×C83 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C83
HallC5×D13 ⋊ C3×C83
HallC5×C13 ⋊ C2×C3×C83
HallC13⋊C3 ⋊ C2×C5×C83
HallD13 ⋊ C3×C5×C83

Subgroups

subgroupG/H
center, hypercenterC5×C83D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C83
FrattiniC1G
Fitting, socleC5×C13×C83C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5395

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 19);