Finite Group Databasebeta

C3×C3121 #22627293

order9363
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C5×C13×C16 (order 6240) · Inn(G) = C1 · Out(G) = C2×C3×C5×C13×C16
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9363
abelianC3×C3121

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9363 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9363, Dic9363, C3⋊#27159676, …
Fitting subgroup ofD3×C3121, C3×D3121, D9363, …
socle ofD3×C3121, C3×D3121, D9363, …
maximal subgroup ofD3×C3121, C3×D3121, D9363, …
maximal normal subgroup ofD3×C3121, C3×D3121, D9363, …
maximal quotient ofC2×C3×C3121, C9×C3121, C32×C3121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9363, 2);