Finite Group Databasebeta

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C23×C3×C251 #72185209

order6024
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 84000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C251
multiplicative(ℤ/10563)ˣ, (ℤ/14084)ˣ, (ℤ/18108)ˣ, (ℤ/21126)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C251, C24×C3×C251, C23×C9×C251, …
maximal normal subgroup ofC22×C3×C4×C251, C24×C3×C251, C23×C9×C251, …
maximal quotient ofC22×C3×C4×C251, C24×C3×C251, C23×C9×C251, …
automorphism group ofC3×C7×C503
outer automorphism group ofC3×C7×C503

GAP

Past the SmallGroups library coverage — no SmallGroups id.