Finite Group Databasebeta

← Prev (#72188123) Next (#72188125) →

C42×C11×C53 #72188124

order9328
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C11×C53
multiplicative(ℤ/11665)ˣ, (ℤ/23330)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C11×C53
socle, prime radicalC22×C11×C53C22
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C8×C11×C53, C2×C42×C11×C53, C3×C42×C11×C53
maximal normal subgroup ofC4×C8×C11×C53, C2×C42×C11×C53, C3×C42×C11×C53
maximal quotient ofC4×C8×C11×C53, C2×C42×C11×C53, C3×C42×C11×C53
automorphism group ofC5×C2333
outer automorphism group ofC5×C2333

GAP

Past the SmallGroups library coverage — no SmallGroups id.