Finite Group Databasebeta

C5×C1901 #23748847

order9505
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C42×C19×C25 (order 7600) · Inn(G) = C1 · Out(G) = C42×C19×C25
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9505
abelianC5×C1901

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9505 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD9505, Dic9505, #49184570, …
Fitting subgroup ofD5×C1901, C5×D1901, D9505, …
socle ofD5×C1901, C5×D1901, D9505, …
maximal subgroup ofD5×C1901, C5×D1901, D9505, …
maximal normal subgroup ofD5×C1901, C5×D1901, D9505, …
maximal quotient ofC2×C5×C1901, C3×C5×C1901

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9505, 2);