Finite Group Databasebeta

← Prev (#23753534) Next (#23753536) →

C2×C11×C17×D13 #23753535

order9724
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C22×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C17×D13
unambiguous semidirect productC13⋊(C22×C11×C17)
unambiguous semidirect product(C2×C13)⋊(C2×C11×C17)

Splittings

Fitting, socleC2×C11×C13×C17 ⋊ C2
derived, SylowC13 ⋊ C22×C11×C17
HallC11×C13×C17 ⋊ C22
HallC13×C17 ⋊ C22×C11
HallC11×C13 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D13
commutator, cosocle, hypocenterC13C22×C11×C17
FrattiniC1G
Fitting, socleC2×C11×C13×C17C2
LCSG ▷ C13
UCSC1 ◁ C2×C11×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C17×D13⋊C3, D3×C11×C17×D13, C2×C3×C11×C17×D13, …
maximal normal subgroup ofC2×C11×C17×D13⋊C3, C2×C3×C11×C17×D13
maximal quotient ofD3×C11×C17×D13, C2×C3×C11×C17×D13, C2×C11×C17×D39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9724, 34);