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C5×C13⋊C3×D83 #44569167

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

Aliases

direct productC5×C13⋊C3×D83
unambiguous semidirect productC83⋊(C2×C5×C13⋊C3)
unambiguous semidirect product(C13×D83)⋊(C3×C5)
unambiguous semidirect product(C5×C13×D83)⋊C3

Splittings

Fitting, socle, HallC5×C13×C83 ⋊ C2×C3
derived, HallC13×C83 ⋊ C2×C3×C5
HallC5×C13⋊C3×C83 ⋊ C2
HallC5×C13×D83 ⋊ C3
HallC13⋊C3×C83 ⋊ C2×C5
HallC13×D83 ⋊ C3×C5
HallC5×C83 ⋊ C2×C13⋊C3
SylowC83 ⋊ C2×C5×C13⋊C3
HallC5×C13 ⋊ C3×D83
SylowC13 ⋊ C3×C5×D83

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×D83
commutator, cosocle, hypocenterC13×C83C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C83C2×C3
LCSG ▷ C13×C83
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5395

Conjugacy classes & character table

1505 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 18);