Finite Group Databasebeta

← Prev (#72193952) Next (#72193954) →

C22×C3×C4×C9×C37 #72193953

order15984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 746496
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C4×C9×C37
multiplicative(ℤ/19817)ˣ, (ℤ/21185)ˣ, (ℤ/24753)ˣ, (ℤ/25479)ˣ, (ℤ/28161)ˣ, (ℤ/28749)ˣ, (ℤ/30105)ˣ, (ℤ/33004)ˣ, (ℤ/38332)ˣ, (ℤ/39634)ˣ, (ℤ/42370)ˣ, (ℤ/49284)ˣ, (ℤ/49506)ˣ, (ℤ/50958)ˣ, (ℤ/56322)ˣ, (ℤ/57498)ˣ, (ℤ/60210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C32×C37
socle, prime radicalC23×C32×C37C2×C3
LCSG ▷ C1
UCSC1 ◁ G

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C9×C37, C2×C3×C42×C9×C37, C23×C3×C4×C9×C37
maximal normal subgroup ofC22×C3×C8×C9×C37, C2×C3×C42×C9×C37, C23×C3×C4×C9×C37
maximal quotient ofC22×C3×C8×C9×C37, C2×C3×C42×C9×C37, C23×C3×C4×C9×C37
automorphism group ofC7×C19×C149, C3×C37×C223, C2×C3×C37×C223, …
outer automorphism group ofC7×C19×C149, C3×C37×C223, C2×C3×C37×C223, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.