Finite Group Databasebeta

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C24×C32×C4×C5×C7 #72197789

order20160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 11890851840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC24×C32×C4×C5×C7
multiplicative(ℤ/49192)ˣ, (ℤ/49665)ˣ, (ℤ/50344)ˣ, (ℤ/51688)ˣ, (ℤ/52976)ˣ, (ℤ/53320)ˣ, (ℤ/56056)ˣ, (ℤ/59080)ˣ, (ℤ/60200)ˣ, (ℤ/60760)ˣ, (ℤ/62952)ˣ, (ℤ/63984)ˣ, (ℤ/64728)ˣ, (ℤ/65832)ˣ, (ℤ/66220)ˣ, (ℤ/66456)ˣ, (ℤ/68112)ˣ, (ℤ/70728)ˣ, (ℤ/70896)ˣ, (ℤ/71568)ˣ, (ℤ/71736)ˣ, (ℤ/72912)ˣ, (ℤ/73788)ˣ, (ℤ/75516)ˣ, (ℤ/75960)ˣ, (ℤ/77400)ˣ, (ℤ/77532)ˣ, (ℤ/77616)ˣ, (ℤ/79980)ˣ, (ℤ/80388)ˣ, (ℤ/84084)ˣ, (ℤ/85140)ˣ, (ℤ/88200)ˣ, (ℤ/88620)ˣ, (ℤ/89460)ˣ, (ℤ/90300)ˣ, (ℤ/91140)ˣ, (ℤ/97020)ˣ, (ℤ/99330)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C32×C5×C7
socle, prime radicalC25×C32×C5×C7C2
LCSG ▷ C1
UCSC1 ◁ G

16344 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

20160 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.