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C22×C3×C4×C5×C7×C11 #72196283

order18480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C5×C7×C11
multiplicative(ℤ/20677)ˣ, (ℤ/21229)ˣ, (ℤ/21373)ˣ, (ℤ/23785)ˣ, (ℤ/24265)ˣ, (ℤ/24563)ˣ, (ℤ/24725)ˣ, (ℤ/25465)ˣ, (ℤ/26015)ˣ, (ℤ/28175)ˣ, (ℤ/28797)ˣ, (ℤ/29049)ˣ, (ℤ/29645)ˣ, (ℤ/31581)ˣ, (ℤ/34665)ˣ, (ℤ/34725)ˣ, (ℤ/36968)ˣ, (ℤ/36976)ˣ, (ℤ/38396)ˣ, (ℤ/38732)ˣ, (ℤ/41354)ˣ, (ℤ/42458)ˣ, (ℤ/42746)ˣ, (ℤ/46220)ˣ, (ℤ/46300)ˣ, (ℤ/47570)ˣ, (ℤ/48530)ˣ, (ℤ/49126)ˣ, (ℤ/49450)ˣ, (ℤ/50930)ˣ, (ℤ/52030)ˣ, (ℤ/55452)ˣ, (ℤ/56350)ˣ, (ℤ/57594)ˣ, (ℤ/58098)ˣ, (ℤ/59290)ˣ, (ℤ/63162)ˣ, (ℤ/69330)ˣ, (ℤ/69450)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C5×C7×C11
socle, prime radicalC23×C3×C5×C7×C11C2
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

18480 conjugacy classes. The character table is too large to display.

Relationships

automorphism group ofC23×C29×C31, C13×C23×C71
outer automorphism group ofC23×C29×C31, C13×C23×C71

GAP

Past the SmallGroups library coverage — no SmallGroups id.