Finite Group Databasebeta

C17×C503 #22555593

order8551
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C16×C251 (order 8032) · Inn(G) = C1 · Out(G) = C2×C16×C251
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8551
abelianC17×C503

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8551 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD8551, Dic8551, C503⋊#595, …
Fitting subgroup ofD17×C503, C17×D503, D8551, …
socle ofD17×C503, C17×D503, D8551, …
maximal subgroup ofD17×C503, C17×D503, D8551, …
maximal normal subgroup ofD17×C503, C17×D503, D8551, …
maximal quotient ofC2×C17×C503, C3×C17×C503

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8551, 1);