Finite Group Databasebeta

C53×C151 #22547893

order8003
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C13×C25 (order 7800) · Inn(G) = C1 · Out(G) = C2×C3×C4×C13×C25
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8003
abelianC53×C151

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8003 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD8003, Dic8003, C151⋊#6157, …
Fitting subgroup ofD53×C151, C53×D151, D8003, …
socle ofD53×C151, C53×D151, D8003, …
maximal subgroup ofD53×C151, C53×D151, D8003, …
maximal normal subgroup ofD53×C151, C53×D151, D8003, …
maximal quotient ofC2×C53×C151, C3×C53×C151

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8003, 1);