Finite Group Databasebeta

C79×C89 #20296362

order7031
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C8×C11×C13 (order 6864) · Inn(G) = C1 · Out(G) = C2×C3×C8×C11×C13
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7031
abelianC79×C89

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7031 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7031, Dic7031, C79⋊#67063, …
Fitting subgroup ofC89×D79, C79×D89, D7031, …
socle ofC89×D79, C79×D89, D7031, …
maximal subgroup ofC89×D79, C79×D89, D7031, …
maximal normal subgroup ofC89×D79, C79×D89, D7031, …
maximal quotient ofC2×C79×C89, C3×C79×C89, C5×C79×C89

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7031, 1);