Finite Group Databasebeta

C43×C191 #22551373

order8213
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C5×C7×C19 (order 7980) · Inn(G) = C1 · Out(G) = C22×C3×C5×C7×C19
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8213
abelianC43×C191

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8213 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD8213, Dic8213, D43×D191, …
Fitting subgroup ofD43×C191, C43×D191, D8213, …
socle ofD43×C191, C43×D191, D8213, …
maximal subgroup ofD43×C191, C43×D191, D8213, …
maximal normal subgroup ofD43×C191, C43×D191, D8213, …
maximal quotient ofC2×C43×C191, C3×C43×C191

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8213, 1);