Finite Group Databasebeta

C11×C719 #21463652

order7909
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C5×C359 (order 7180) · Inn(G) = C1 · Out(G) = C22×C5×C359
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7909
abelianC11×C719

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7909 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7909, Dic7909, D11×D719, …
Fitting subgroup ofD11×C719, C11×D719, D7909, …
socle ofD11×C719, C11×D719, D7909, …
maximal subgroup ofD11×C719, C11×D719, D7909, …
maximal normal subgroup ofD11×C719, C11×D719, D7909, …
maximal quotient ofC2×C11×C719, C3×C11×C719

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7909, 1);