Finite Group Databasebeta

C3×C2687 #22549014

order8061
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C17×C79 (order 5372) · Inn(G) = C1 · Out(G) = C22×C17×C79
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8061
abelianC3×C2687

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8061 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD8061, Dic8061, D3×D2687, …
Fitting subgroup ofD3×C2687, C3×D2687, D8061, …
socle ofD3×C2687, C3×D2687, D8061, …
maximal subgroup ofD3×C2687, C3×D2687, D8061, …
maximal normal subgroup ofD3×C2687, C3×D2687, D8061, …
maximal quotient ofC2×C3×C2687, C9×C2687, C32×C2687, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8061, 1);