Finite Group Databasebeta

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C22×C3×C42×C5×C25 #72201287

order24000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 589824000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4×C5

Aliases

abelianC22×C3×C42×C5×C25
multiplicative(ℤ/38885)ˣ, (ℤ/43329)ˣ, (ℤ/46965)ˣ, (ℤ/49288)ˣ, (ℤ/49995)ˣ, (ℤ/50096)ˣ, (ℤ/53025)ˣ, (ℤ/53625)ˣ, (ℤ/57772)ˣ, (ℤ/60400)ˣ, (ℤ/61000)ˣ, (ℤ/62000)ˣ, (ℤ/62620)ˣ, (ℤ/70700)ˣ, (ℤ/71500)ˣ, (ℤ/73932)ˣ, (ℤ/77770)ˣ, (ℤ/86658)ˣ, (ℤ/90900)ˣ, (ℤ/91500)ˣ, (ℤ/93930)ˣ, (ℤ/99990)ˣ, (ℤ/106050)ˣ, (ℤ/107250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C5C24×C3×C52
socle, prime radicalC24×C3×C52C22×C5
LCSG ▷ C1
UCSC1 ◁ G

6972 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24000 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.