Finite Group Databasebeta

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C23×C3×C42×C7×C9 #72201490

order24192
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 42807066624
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C3×C4

Aliases

abelianC23×C3×C42×C7×C9
multiplicative(ℤ/57304)ˣ, (ℤ/57855)ˣ, (ℤ/60088)ˣ, (ℤ/61712)ˣ, (ℤ/63640)ˣ, (ℤ/65360)ˣ, (ℤ/66040)ˣ, (ℤ/71120)ˣ, (ℤ/72520)ˣ, (ℤ/74480)ˣ, (ℤ/76368)ˣ, (ℤ/77140)ˣ, (ℤ/77256)ˣ, (ℤ/79248)ˣ, (ℤ/79344)ˣ, (ℤ/81432)ˣ, (ℤ/85956)ˣ, (ℤ/87024)ˣ, (ℤ/87696)ˣ, (ℤ/90132)ˣ, (ℤ/91440)ˣ, (ℤ/92880)ˣ, (ℤ/95460)ˣ, (ℤ/99060)ˣ, (ℤ/99180)ˣ, (ℤ/105840)ˣ, (ℤ/108780)ˣ, (ℤ/109620)ˣ, (ℤ/115710)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C25×C32×C7
socle, prime radicalC25×C32×C7C22×C3
LCSG ▷ C1
UCSC1 ◁ G

30000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24192 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.