Finite Group Databasebeta

C7×C1319 #22604433

order9233
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C659 (order 7908) · Inn(G) = C1 · Out(G) = C22×C3×C659
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9233
abelianC7×C1319

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9233 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9233, Dic9233, D7×D1319, …
Fitting subgroup ofD7×C1319, C7×D1319, D9233, …
socle ofD7×C1319, C7×D1319, D9233, …
maximal subgroup ofD7×C1319, C7×D1319, D9233, …
maximal normal subgroup ofD7×C1319, C7×D1319, D9233, …
maximal quotient ofC2×C7×C1319, C3×C7×C1319

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9233, 1);