Finite Group Databasebeta

C3×C3067 #22604162

order9201
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C7×C73 (order 6132) · Inn(G) = C1 · Out(G) = C22×C3×C7×C73
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9201
abelianC3×C3067

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9201 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9201, Dic9201, D3×D3067, …
Fitting subgroup ofD3×C3067, C3×D3067, D9201, …
socle ofD3×C3067, C3×D3067, D9201, …
maximal subgroup ofD3×C3067, C3×D3067, D9201, …
maximal normal subgroup ofD3×C3067, C3×D3067, D9201, …
maximal quotient ofC2×C3×C3067, C9×C3067, C32×C3067, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9201, 2);