Finite Group Databasebeta

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C23×C11×C23 #72182012

order2024
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 36960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C11×C23
multiplicative(ℤ/3243)ˣ, (ℤ/4232)ˣ, (ℤ/4324)ˣ, (ℤ/6348)ˣ, (ℤ/6486)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C11×C23, C22×C4×C11×C23, C23×C3×C11×C23, …
maximal normal subgroup ofC24×C11×C23, C22×C4×C11×C23, C23×C3×C11×C23, …
maximal quotient ofC24×C11×C23, C22×C4×C11×C23, C23×C3×C11×C23, …
automorphism group ofC3×C23×C47, C4×C23×C47, C3×C4×C529, …
outer automorphism group ofC3×C23×C47, C4×C23×C47, C3×C4×C529, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.