Finite Group Databasebeta

← Prev (#31824970) Next (#31824972) →

C7×D1287 #31824971

order18018
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1287
unambiguous semidirect productC9⋊(C7×D143)
unambiguous semidirect productC11⋊(C7×D117)
unambiguous semidirect productC13⋊(C7×D99)

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C2
derived, HallC9×C11×C13 ⋊ C2×C7
HallC7×C11×C13 ⋊ D9
HallC7×C9×C13 ⋊ D11
HallC7×C9×C11 ⋊ D13
HallC11×C13 ⋊ C7×D9
HallC9×C13 ⋊ C7×D11
HallC9×C11 ⋊ C7×D13
HallC7×C13 ⋊ D99
HallC7×C11 ⋊ D117
HallC7×C9 ⋊ D143
SylowC13 ⋊ C7×D99
SylowC11 ⋊ C7×D117
SylowC9 ⋊ C7×D143

Subgroups

subgroupG/H
center, hypercenterC7D1287
commutator, cosocle, hypocenterC9×C11×C13C2×C7
FrattiniC3C7×D429
FittingC7×C9×C11×C13C2
socleC3×C7×C11×C13D3
LCSG ▷ C9×C11×C13
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

4515 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D13×D99, C7×D11×D117, C7×D9×D143, …
maximal normal subgroup ofC7×D13×D99, C7×D11×D117, C7×D9×D143, …
maximal quotient ofC7×Dic1287, C2×C7×D1287

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 16);