Finite Group Databasebeta

C29×C311 #22583129

order9019
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C5×C7×C31 (order 8680) · Inn(G) = C1 · Out(G) = C2×C4×C5×C7×C31
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9019
abelianC29×C311

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9019 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9019, Dic9019, C311⋊#1181, …
Fitting subgroup ofD29×C311, C29×D311, D9019, …
socle ofD29×C311, C29×D311, D9019, …
maximal subgroup ofD29×C311, C29×D311, D9019, …
maximal normal subgroup ofD29×C311, C29×D311, D9019, …
maximal quotient ofC2×C29×C311, C3×C29×C311

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9019, 1);