Finite Group Databasebeta

← Prev (#72186368) Next (#72186370) →

C24×C17×C27 #72186369

order7344
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5806080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C17×C27
multiplicative(ℤ/22056)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C24×C3×C17
socle, prime radicalC24×C3×C17C9
LCSG ▷ C1
UCSC1 ◁ G

536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7344 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C17×C27, C25×C17×C27, C24×C17×C81, …
maximal normal subgroup ofC23×C4×C17×C27, C25×C17×C27, C24×C17×C81, …
maximal quotient ofC23×C4×C17×C27, C25×C17×C27, C24×C17×C81, …
automorphism group ofC3×C8×C919
outer automorphism group ofC3×C8×C919

GAP

Past the SmallGroups library coverage — no SmallGroups id.