Finite Group Databasebeta

C7×C991 #20294221

order6937
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C5×C9×C11 (order 5940) · Inn(G) = C1 · Out(G) = C22×C3×C5×C9×C11
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC6937
abelianC7×C991

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6937 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD6937, #35209539, #35209540, …
Fitting subgroup ofD7×C991, C7×D991, D6937, …
socle ofD7×C991, C7×D991, D6937, …
maximal subgroup ofD7×C991, C7×D991, D6937, …
maximal normal subgroup ofD7×C991, C7×D991, D6937, …
maximal quotient ofC2×C7×C991, C3×C7×C991, C5×C7×C991

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6937, 1);