Finite Group Databasebeta

← Prev (#45688675) Next (#45688677) →

C3×C17⋊(D109⋊C3) #45688676

order33354
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17⋊(D109⋊C3)
unambiguous semidirect productC17⋊(C3×D109⋊C3)
unambiguous semidirect product(C109⋊C3)⋊(C3×D17)
unambiguous semidirect productD1853⋊C32
unambiguous semidirect product(C3×D1853)⋊C3

Splittings

Fitting, socleC3×C17×C109 ⋊ C2×C3
derived, HallC17×C109 ⋊ C2×C32
HallC3×C17×C109⋊C3 ⋊ C2
HallD1853 ⋊ C32
HallC3×C109⋊C3 ⋊ D17
SylowC109 ⋊ C32×D17
SylowC17 ⋊ C3×D109⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C17⋊(D109⋊C3)
commutator, cosocle, hypocenterC17×C109C2×C32
FrattiniC1G
Fitting, socleC3×C17×C109C2×C3
LCSG ▷ C17×C109
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5559

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33354, 19);