Finite Group Databasebeta

← Prev (#45684133) Next (#45684135) →

C17×D975 #45684134

order33150
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D975
unambiguous semidirect productC3⋊(C17×D325)
unambiguous semidirect productC13⋊(C17×D75)
unambiguous semidirect productC25⋊(C17×D39)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, HallC3×C13×C25 ⋊ C2×C17
HallC13×C17×C25 ⋊ D3
HallC3×C17×C25 ⋊ D13
HallC3×C13×C17 ⋊ D25
HallC17×C25 ⋊ D39
HallC13×C25 ⋊ D3×C17
HallC13×C17 ⋊ D75
HallC3×C25 ⋊ C17×D13
HallC3×C17 ⋊ D325
HallC3×C13 ⋊ C17×D25
SylowC25 ⋊ C17×D39
SylowC13 ⋊ C17×D75
SylowC3 ⋊ C17×D325

Subgroups

subgroupG/H
center, hypercenterC17D975
commutator, cosocle, hypocenterC3×C13×C25C2×C17
FrattiniC5C17×D195
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17D5
LCSG ▷ C3×C13×C25
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

8313 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 16);