Finite Group Databasebeta

C3×C3169 #23748859

order9507
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C9×C11×C32 (order 6336) · Inn(G) = C1 · Out(G) = C2×C9×C11×C32
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9507
abelianC3×C3169

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9507 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9507, Dic9507, C3⋊#27162786, …
Fitting subgroup ofD3×C3169, C3×D3169, D9507, …
socle ofD3×C3169, C3×D3169, D9507, …
maximal subgroup ofD3×C3169, C3×D3169, D9507, …
maximal normal subgroup ofD3×C3169, C3×D3169, D9507, …
maximal quotient ofC2×C3×C3169, C9×C3169, C32×C3169, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9507, 2);