Finite Group Databasebeta

← Prev (#72186557) Next (#72186559) →

C23×C7×C8×C17 #72186558

order7616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4128768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C7×C8×C17
multiplicative(ℤ/22872)ˣ, (ℤ/22944)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C7×C17
socle, prime radicalC24×C7×C17C4
LCSG ▷ C1
UCSC1 ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C7×C16×C17, C22×C4×C7×C8×C17, C24×C7×C8×C17, …
maximal normal subgroup ofC23×C7×C16×C17, C22×C4×C7×C8×C17, C24×C7×C8×C17, …
maximal quotient ofC23×C7×C16×C17, C22×C4×C7×C8×C17, C24×C7×C8×C17, …
automorphism group ofC3×C8×C953, C3×C32×C239
outer automorphism group ofC3×C8×C953, C3×C32×C239

GAP

Past the SmallGroups library coverage — no SmallGroups id.