Finite Group Databasebeta

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C22×C32×C5×C7×C16 #72197776

order20160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 884736
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C5×C7×C16
multiplicative(ℤ/22661)ˣ, (ℤ/24521)ˣ, (ℤ/25109)ˣ, (ℤ/25823)ˣ, (ℤ/25949)ˣ, (ℤ/31089)ˣ, (ℤ/31341)ˣ, (ℤ/31527)ˣ, (ℤ/32283)ˣ, (ℤ/33363)ˣ, (ℤ/35427)ˣ, (ℤ/41452)ˣ, (ℤ/41788)ˣ, (ℤ/45322)ˣ, (ℤ/47236)ˣ, (ℤ/49042)ˣ, (ℤ/50218)ˣ, (ℤ/51646)ˣ, (ℤ/51898)ˣ, (ℤ/62178)ˣ, (ℤ/62682)ˣ, (ℤ/63054)ˣ, (ℤ/64566)ˣ, (ℤ/66726)ˣ, (ℤ/70854)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C32×C5×C7
socle, prime radicalC23×C32×C5×C7C8
LCSG ▷ C1
UCSC1 ◁ G

1176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

automorphism group ofC17×C31×C43
outer automorphism group ofC17×C31×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.