Finite Group Databasebeta

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C22×C3×C4×C16×C25 #72196891

order19200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15728640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C3×C4×C16×C25
multiplicative(ℤ/36057)ˣ, (ℤ/38505)ˣ, (ℤ/41072)ˣ, (ℤ/41704)ˣ, (ℤ/42105)ˣ, (ℤ/44625)ˣ, (ℤ/44912)ˣ, (ℤ/45248)ˣ, (ℤ/48040)ˣ, (ℤ/48076)ˣ, (ℤ/48320)ˣ, (ℤ/51340)ˣ, (ℤ/56000)ˣ, (ℤ/56140)ˣ, (ℤ/57648)ˣ, (ℤ/57744)ˣ, (ℤ/58176)ˣ, (ℤ/59500)ˣ, (ℤ/61812)ˣ, (ℤ/62556)ˣ, (ℤ/72000)ˣ, (ℤ/72060)ˣ, (ℤ/72114)ˣ, (ℤ/72180)ˣ, (ℤ/76500)ˣ, (ℤ/77010)ˣ, (ℤ/84210)ˣ, (ℤ/89250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5×C8C24×C3×C5
socle, prime radicalC24×C3×C5C2×C5×C8
LCSG ▷ C1
UCSC1 ◁ G

3066 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

19200 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.