Finite Group Databasebeta

← Prev (#72201085) Next (#72201087) →

C24×C3×C5×C9×C11 #72201086

order23760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 87091200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC24×C3×C5×C9×C11
multiplicative(ℤ/33649)ˣ, (ℤ/40641)ˣ, (ℤ/42009)ˣ, (ℤ/43263)ˣ, (ℤ/45969)ˣ, (ℤ/47817)ˣ, (ℤ/48279)ˣ, (ℤ/49352)ˣ, (ℤ/50312)ˣ, (ℤ/54188)ˣ, (ℤ/55496)ˣ, (ℤ/56012)ˣ, (ℤ/61292)ˣ, (ℤ/64372)ˣ, (ℤ/67298)ˣ, (ℤ/71352)ˣ, (ℤ/71496)ˣ, (ℤ/74028)ˣ, (ℤ/75468)ˣ, (ℤ/77004)ˣ, (ℤ/78804)ˣ, (ℤ/79596)ˣ, (ℤ/81282)ˣ, (ℤ/82764)ˣ, (ℤ/83244)ˣ, (ℤ/84018)ˣ, (ℤ/86526)ˣ, (ℤ/91476)ˣ, (ℤ/91938)ˣ, (ℤ/95634)ˣ, (ℤ/96558)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C24×C32×C5×C11
socle, prime radicalC24×C32×C5×C11C3
LCSG ▷ C1
UCSC1 ◁ G

2680 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

23760 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.