Finite Group Databasebeta

← Prev (#72190373) Next (#72190375) →

C23×C8×C11×C17 #72190374

order11968
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6881280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C8×C11×C17
multiplicative(ℤ/25208)ˣ, (ℤ/37812)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C11×C17
socle, prime radicalC24×C11×C17C4
LCSG ▷ C1
UCSC1 ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C11×C16×C17, C24×C8×C11×C17, C22×C4×C8×C11×C17
maximal normal subgroup ofC23×C11×C16×C17, C24×C8×C11×C17, C22×C4×C8×C11×C17
maximal quotient ofC23×C11×C16×C17, C24×C8×C11×C17, C22×C4×C8×C11×C17
automorphism group ofC8×C23×C137
outer automorphism group ofC8×C23×C137

GAP

Past the SmallGroups library coverage — no SmallGroups id.