Finite Group Databasebeta

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C22×C11×C256 #72189752

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 122880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C11×C256
multiplicative(ℤ/17733)ˣ, (ℤ/23552)ˣ, (ℤ/23644)ˣ, (ℤ/35466)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC128C23×C11
socle, prime radicalC23×C11C128
LCSG ▷ C1
UCSC1 ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11×C512, C23×C11×C256, C2×C4×C11×C256
maximal normal subgroup ofC22×C11×C512, C23×C11×C256, C2×C4×C11×C256
maximal quotient ofC22×C11×C512, C23×C11×C256, C2×C4×C11×C256
automorphism group ofC23×C1024
outer automorphism group ofC23×C1024

GAP

Past the SmallGroups library coverage — no SmallGroups id.