Finite Group Databasebeta

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C23×C32×C83 #72185176

order5976
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 661248
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C32×C83
multiplicative(ℤ/10479)ˣ, (ℤ/10521)ˣ, (ℤ/13972)ˣ, (ℤ/17964)ˣ, (ℤ/20958)ˣ, (ℤ/21042)ˣ

Subgroups

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

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5976 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C83, C24×C32×C83, C23×C3×C9×C83, …
maximal normal subgroup ofC22×C32×C4×C83, C24×C32×C83, C23×C3×C9×C83, …
maximal quotient ofC22×C32×C4×C83, C24×C32×C83, C23×C3×C9×C83, …
automorphism group ofC3×C7×C499, C7×C9×C167
outer automorphism group ofC3×C7×C499, C7×C9×C167

GAP

Past the SmallGroups library coverage — no SmallGroups id.