Finite Group Databasebeta

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C23×C3×C5×C11×C16 #72198688

order21120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6881280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C5×C11×C16
multiplicative(ℤ/30107)ˣ, (ℤ/36363)ˣ, (ℤ/37587)ˣ, (ℤ/38709)ˣ, (ℤ/43197)ˣ, (ℤ/44344)ˣ, (ℤ/45016)ˣ, (ℤ/45632)ˣ, (ℤ/47168)ˣ, (ℤ/48484)ˣ, (ℤ/49336)ˣ, (ℤ/50116)ˣ, (ℤ/54208)ˣ, (ℤ/57596)ˣ, (ℤ/60214)ˣ, (ℤ/63432)ˣ, (ℤ/63552)ˣ, (ℤ/66516)ˣ, (ℤ/67524)ˣ, (ℤ/69696)ˣ, (ℤ/72726)ˣ, (ℤ/74004)ˣ, (ℤ/74052)ˣ, (ℤ/75174)ˣ, (ℤ/77418)ˣ, (ℤ/86394)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C24×C3×C5×C11
socle, prime radicalC24×C3×C5×C11C8
LCSG ▷ C1
UCSC1 ◁ G

1760 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

21120 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.