Finite Group Databasebeta

← Prev (#72185282) Next (#72185284) →

C23×C32×C5×C17 #72185283

order6120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 516096
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C32×C5×C17
multiplicative(ℤ/7931)ˣ, (ℤ/9579)ˣ, (ℤ/10197)ˣ, (ℤ/12772)ˣ, (ℤ/15862)ˣ, (ℤ/19158)ˣ, (ℤ/20394)ˣ

Subgroups

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

384 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C5×C17, C24×C32×C5×C17, C23×C3×C5×C9×C17, …
maximal normal subgroup ofC22×C32×C4×C5×C17, C24×C32×C5×C17, C23×C3×C5×C9×C17, …
maximal quotient ofC22×C32×C4×C5×C17, C24×C32×C5×C17, C23×C3×C5×C9×C17, …
automorphism group ofC7×C11×C103, C3×C31×C103, C9×C11×C103
outer automorphism group ofC7×C11×C103, C3×C31×C103, C9×C11×C103

GAP

Past the SmallGroups library coverage — no SmallGroups id.