Finite Group Databasebeta

C3×C2593 #21441147

order7779
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C32×C81 (order 5184) · Inn(G) = C1 · Out(G) = C2×C32×C81
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7779
abelianC3×C2593

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7779 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7779, Dic7779, C3⋊#23780505, …
Fitting subgroup ofD3×C2593, C3×D2593, D7779, …
socle ofD3×C2593, C3×D2593, D7779, …
maximal subgroup ofD3×C2593, C3×D2593, D7779, …
maximal normal subgroup ofD3×C2593, C3×D2593, D7779, …
maximal quotient ofC2×C3×C2593, C9×C2593, C32×C2593, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7779, 2);