Finite Group Databasebeta

← Prev (#45684196) Next (#45684198) →

C17×C3⋊(C5⋊D65) #45684197

order33150
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C5

Aliases

direct productC17×C3⋊(C5⋊D65)
unambiguous semidirect productC3⋊(C17×C5⋊D65)
unambiguous semidirect productC5⋊(C17×D195)
unambiguous semidirect productC13⋊(C17×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C13×C17 ⋊ C2
derived, HallC3×C52×C13 ⋊ C2×C17
HallC52×C13×C17 ⋊ D3
HallC3×C52×C17 ⋊ D13
HallC3×C13×C17 ⋊ C5⋊D5
HallC52×C17 ⋊ D39
HallC52×C13 ⋊ D3×C17
HallC13×C17 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C17×D13
HallC3×C17 ⋊ C5⋊D65
HallC3×C13 ⋊ C17×C5⋊D5
SylowC52 ⋊ C17×D39
SylowC13 ⋊ C17×C3⋊(C5⋊D5)
SylowC3 ⋊ C17×C5⋊D65

Subgroups

subgroupG/H
center, hypercenterC17C3⋊(C5⋊D65)
commutator, cosocle, hypocenterC3×C52×C13C2×C17
FrattiniC1G
Fitting, socleC3×C52×C13×C17C2
LCSG ▷ C3×C52×C13
UCSC1 ◁ C17

128 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, 79);