Finite Group Databasebeta

← Prev (#46801347) Next (#46801349) →

C11×C17×D91 #46801348

order34034
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×D91
unambiguous semidirect productC7⋊(C11×C17×D13)
unambiguous semidirect productC13⋊(C11×D7×C17)

Splittings

Fitting, socle, HallC7×C11×C13×C17 ⋊ C2
derived, HallC7×C13 ⋊ C2×C11×C17
HallC11×C13×C17 ⋊ D7
HallC7×C13×C17 ⋊ C2×C11
HallC7×C11×C17 ⋊ D13
HallC7×C11×C13 ⋊ C2×C17
HallC13×C17 ⋊ C11×D7
HallC11×C13 ⋊ D7×C17
HallC7×C17 ⋊ C11×D13
HallC7×C11 ⋊ C17×D13
SylowC13 ⋊ C11×D7×C17
SylowC7 ⋊ C11×C17×D13

Subgroups

subgroupG/H
center, hypercenterC11×C17D91
commutator, cosocle, hypocenterC7×C13C2×C11×C17
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C7×C13
UCSC1 ◁ C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

8789 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 11);