Finite Group Databasebeta

← Prev (#23779604) Next (#23779606) →

C22×C11×C233 #23779605

order10252
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C11×C233
multiplicative(ℤ/10741)ˣ, (ℤ/21482)ˣ

Subgroups

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

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10252 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC11×A4×C233
socle ofC11×A4×C233
maximal subgroup ofC22×C3×C11×C233, C11×A4×C233, C2×D3×C11×C233, …
maximal normal subgroup ofC22×C3×C11×C233, C11×A4×C233, C2×C4×C11×C233, …
maximal quotient ofC22×C3×C11×C233, C2×D3×C11×C233, C2×C4×C11×C233, …
automorphism group ofC23×C467
outer automorphism group ofC23×C467

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10252, 5);