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C22×C11×C243 #72189243

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C11×C243
multiplicative(ℤ/11201)ˣ, (ℤ/16041)ˣ, (ℤ/16767)ˣ, (ℤ/21388)ˣ, (ℤ/22402)ˣ, (ℤ/32082)ˣ, (ℤ/33534)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC81C22×C3×C11
socle, prime radicalC22×C3×C11C81
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10692 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C11×C243, C23×C11×C243, C22×C11×C729, …
maximal normal subgroup ofC2×C4×C11×C243, C23×C11×C243, C22×C11×C729, …
maximal quotient ofC2×C4×C11×C243, C23×C11×C243, C22×C11×C729, …
automorphism group ofC23×C487
outer automorphism group ofC23×C487

GAP

Past the SmallGroups library coverage — no SmallGroups id.