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C83×C5⋊(D13⋊C3) #44569172

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

Aliases

direct productC83×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(D13⋊C3×C83)
unambiguous semidirect product(C13⋊C3)⋊(D5×C83)
unambiguous semidirect productD65⋊(C3×C83)
unambiguous semidirect product(C83×D65)⋊C3

Splittings

Fitting, socle, HallC5×C13×C83 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C83
HallC5×C13⋊C3×C83 ⋊ C2
HallC83×D65 ⋊ C3
HallC13⋊C3×C83 ⋊ D5
HallC13×C83 ⋊ C3×D5
HallC5×C83 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C2×C83
HallD65 ⋊ C3×C83
HallC13⋊C3 ⋊ D5×C83
SylowC13 ⋊ C3×D5×C83
SylowC5 ⋊ D13⋊C3×C83

Subgroups

subgroupG/H
center, hypercenterC83C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C2×C3×C83
FrattiniC1G
Fitting, socleC5×C13×C83C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5395

Conjugacy classes & character table

1826 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 23);