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C22×C32×C4×C5×C23 #72194576

order16560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 811008
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C4×C5×C23
multiplicative(ℤ/18941)ˣ, (ℤ/19877)ˣ, (ℤ/20069)ˣ, (ℤ/21329)ˣ, (ℤ/21545)ˣ, (ℤ/24185)ˣ, (ℤ/24325)ˣ, (ℤ/25437)ˣ, (ℤ/25761)ˣ, (ℤ/25803)ˣ, (ℤ/26949)ˣ, (ℤ/27423)ˣ, (ℤ/29001)ˣ, (ℤ/29043)ˣ, (ℤ/31095)ˣ, (ℤ/31275)ˣ, (ℤ/33916)ˣ, (ℤ/34348)ˣ, (ℤ/35932)ˣ, (ℤ/37882)ˣ, (ℤ/38668)ˣ, (ℤ/39754)ˣ, (ℤ/40138)ˣ, (ℤ/42658)ˣ, (ℤ/43090)ˣ, (ℤ/48370)ˣ, (ℤ/48650)ˣ, (ℤ/49716)ˣ, (ℤ/50874)ˣ, (ℤ/51522)ˣ, (ℤ/51606)ˣ, (ℤ/53898)ˣ, (ℤ/54846)ˣ, (ℤ/58002)ˣ, (ℤ/58086)ˣ, (ℤ/62190)ˣ, (ℤ/62550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C5×C23
socle, prime radicalC23×C32×C5×C23C2
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16560 conjugacy classes. The character table is too large to display.

Relationships

automorphism group ofC13×C31×C47, C11×C13×C139, C7×C47×C61, …
outer automorphism group ofC13×C31×C47, C11×C13×C139, C7×C47×C61, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.