Finite Group Databasebeta

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C23×C3×C42×C5×C13 #72202192

order24960
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6341787648
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C42×C5×C13
multiplicative(ℤ/60632)ˣ, (ℤ/61215)ˣ, (ℤ/65296)ˣ, (ℤ/65720)ˣ, (ℤ/68120)ˣ, (ℤ/69080)ˣ, (ℤ/69520)ˣ, (ℤ/73360)ˣ, (ℤ/74200)ˣ, (ℤ/74360)ˣ, (ℤ/77592)ˣ, (ℤ/78864)ˣ, (ℤ/81620)ˣ, (ℤ/81744)ˣ, (ℤ/82896)ˣ, (ℤ/83952)ˣ, (ℤ/89232)ˣ, (ℤ/90948)ˣ, (ℤ/94200)ˣ, (ℤ/94320)ˣ, (ℤ/94800)ˣ, (ℤ/95400)ˣ, (ℤ/98580)ˣ, (ℤ/101400)ˣ, (ℤ/102180)ˣ, (ℤ/103620)ˣ, (ℤ/104940)ˣ, (ℤ/111300)ˣ, (ℤ/111540)ˣ, (ℤ/122430)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C25×C3×C5×C13
socle, prime radicalC25×C3×C5×C13C22
LCSG ▷ C1
UCSC1 ◁ G

12000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24960 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.