Finite Group Databasebeta

C37×C257 #23748865

order9509
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C4×C9×C256 (order 9216) · Inn(G) = C1 · Out(G) = C4×C9×C256
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9509
abelianC37×C257

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9509 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9509, Dic9509, #49184737, …
Fitting subgroup ofD37×C257, C37×D257, D9509, …
socle ofD37×C257, C37×D257, D9509, …
maximal subgroup ofD37×C257, C37×D257, D9509, …
maximal normal subgroup ofD37×C257, C37×D257, D9509, …
maximal quotient ofC2×C37×C257, C3×C37×C257

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9509, 1);