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C83×D195 #44569165

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

Aliases

direct productC83×D195
unambiguous semidirect productC3⋊(C83×D65)
unambiguous semidirect productC5⋊(D39×C83)
unambiguous semidirect productC13⋊(D15×C83)

Splittings

Fitting, socle, HallC3×C5×C13×C83 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C83
HallC5×C13×C83 ⋊ D3
HallC3×C13×C83 ⋊ D5
HallC3×C5×C83 ⋊ D13
HallC13×C83 ⋊ D15
HallC5×C83 ⋊ D39
HallC3×C83 ⋊ D65
HallC5×C13 ⋊ D3×C83
HallC3×C13 ⋊ D5×C83
HallC3×C5 ⋊ D13×C83
SylowC13 ⋊ D15×C83
SylowC5 ⋊ D39×C83
SylowC3 ⋊ C83×D65

Subgroups

subgroupG/H
center, hypercenterC83D195
commutator, cosocle, hypocenterC3×C5×C13C2×C83
FrattiniC1G
Fitting, socleC3×C5×C13×C83C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16185

Conjugacy classes & character table

8217 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 16);