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C23×C3×C11×C41 #72189390

order10824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 134400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C11×C41
multiplicative(ℤ/13363)ˣ, (ℤ/16683)ˣ, (ℤ/17181)ˣ, (ℤ/21656)ˣ, (ℤ/22244)ˣ, (ℤ/26726)ˣ, (ℤ/32484)ˣ, (ℤ/33366)ˣ, (ℤ/34362)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C11×C41, C22×C3×C4×C11×C41, C23×C9×C11×C41, …
maximal normal subgroup ofC24×C3×C11×C41, C22×C3×C4×C11×C41, C23×C9×C11×C41, …
maximal quotient ofC24×C3×C11×C41, C22×C3×C4×C11×C41, C23×C9×C11×C41, …
automorphism group ofC7×C23×C83
outer automorphism group ofC7×C23×C83

GAP

Past the SmallGroups library coverage — no SmallGroups id.