Finite Group Databasebeta

← Prev (#49112590) Next (#49112592) →

C11×C5⋊(D109⋊C3) #49112591

order35970
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊(D109⋊C3)
unambiguous semidirect productC5⋊(C11×D109⋊C3)
unambiguous semidirect product(C109⋊C3)⋊(D5×C11)
unambiguous semidirect productD545⋊(C3×C11)
unambiguous semidirect product(C11×D545)⋊C3

Splittings

Fitting, socle, HallC5×C11×C109 ⋊ C2×C3
derived, HallC5×C109 ⋊ C2×C3×C11
HallC5×C11×C109⋊C3 ⋊ C2
HallC11×D545 ⋊ C3
HallC11×C109⋊C3 ⋊ D5
HallC5×C109⋊C3 ⋊ C2×C11
HallC11×C109 ⋊ C3×D5
HallD545 ⋊ C3×C11
HallC109⋊C3 ⋊ D5×C11
SylowC109 ⋊ C3×D5×C11
HallC5×C11 ⋊ D109⋊C3
SylowC5 ⋊ C11×D109⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(D109⋊C3)
commutator, cosocle, hypocenterC5×C109C2×C3×C11
FrattiniC1G
Fitting, socleC5×C11×C109C2×C3
LCSG ▷ C5×C109
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5995

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 31);