Finite Group Databasebeta

C53×C179 #23748693

order9487
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C13×C89 (order 9256) · Inn(G) = C1 · Out(G) = C2×C4×C13×C89
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9487
abelianC53×C179

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9487 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9487, Dic9487, C179⋊#6157, …
Fitting subgroup ofD53×C179, C53×D179, D9487, …
socle ofD53×C179, C53×D179, D9487, …
maximal subgroup ofD53×C179, C53×D179, D9487, …
maximal normal subgroup ofD53×C179, C53×D179, D9487, …
maximal quotient ofC2×C53×C179, C3×C53×C179

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9487, 1);