Finite Group Databasebeta

← Prev (#72185485) Next (#72185487) →

C2×C32×C11×C32 #72185486

order6336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 30720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C32×C11×C32
multiplicative(ℤ/6499)ˣ, (ℤ/12998)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C32×C11
socle, prime radicalC22×C32×C11C16
LCSG ▷ C1
UCSC1 ◁ G

204 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C11×C64, C32×C4×C11×C32, C22×C32×C11×C32, …
maximal normal subgroup ofC2×C32×C11×C64, C32×C4×C11×C32, C22×C32×C11×C32, …
maximal quotient ofC2×C32×C11×C64, C32×C4×C11×C32, C22×C32×C11×C32, …
automorphism group ofC67×C97
outer automorphism group ofC67×C97

GAP

Past the SmallGroups library coverage — no SmallGroups id.