Finite Group Databasebeta

C41×C193 #21463670

order7913
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C3×C5×C8×C64 (order 7680) · Inn(G) = C1 · Out(G) = C3×C5×C8×C64
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7913
abelianC41×C193

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7913 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7913, Dic7913, #44539587, …
Fitting subgroup ofD41×C193, C41×D193, D7913, …
socle ofD41×C193, C41×D193, D7913, …
maximal subgroup ofD41×C193, C41×D193, D7913, …
maximal normal subgroup ofD41×C193, C41×D193, D7913, …
maximal quotient ofC2×C41×C193, C3×C41×C193

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7913, 1);