Finite Group Databasebeta

← Prev (#72183192) Next (#72183194) →

C23×C32×C72 #72183193

order3528
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 16257024
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3×C7

Aliases

abelianC23×C32×C72
multiplicative(ℤ/6321)ˣ, (ℤ/8428)ˣ, (ℤ/12642)ˣ

Subgroups

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

960 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C72, C24×C32×C72, C23×C3×C72×C9, …
maximal normal subgroup ofC22×C32×C4×C72, C24×C32×C72, C23×C3×C72×C9, …
maximal quotient ofC22×C32×C4×C72, C24×C32×C72, C23×C3×C72×C9, …
automorphism group ofC3×C43×C49, C4×C43×C49
outer automorphism group ofC3×C43×C49, C4×C43×C49

GAP

Past the SmallGroups library coverage — no SmallGroups id.