Finite Group Databasebeta

← Prev (#72189768) Next (#72189770) →

C22×C11×C162 #72189769

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 377487360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C16

Aliases

abelianC22×C11×C162
multiplicative(ℤ/25024)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC82C24×C11
socle, prime radicalC24×C11C82
LCSG ▷ C1
UCSC1 ◁ G

3146 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×C16×C32, C2×C4×C11×C162, C23×C11×C162
maximal normal subgroup ofC22×C11×C16×C32, C2×C4×C11×C162, C23×C11×C162
maximal quotient ofC22×C11×C16×C32, C2×C4×C11×C162, C23×C11×C162
automorphism group ofC17×C23×C64
outer automorphism group ofC17×C23×C64

GAP

Past the SmallGroups library coverage — no SmallGroups id.