Finite Group Databasebeta

C59×C139 #22551335

order8201
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C23×C29 (order 8004) · Inn(G) = C1 · Out(G) = C22×C3×C23×C29
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8201
abelianC59×C139

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8201 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD8201, Dic8201, D59×D139, …
Fitting subgroup ofD59×C139, C59×D139, D8201, …
socle ofD59×C139, C59×D139, D8201, …
maximal subgroup ofD59×C139, C59×D139, D8201, …
maximal normal subgroup ofD59×C139, C59×D139, D8201, …
maximal quotient ofC2×C59×C139, C3×C59×C139

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8201, 1);