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C22×C3×C4×C5×C7×C9 #72193154

order15120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 497664
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C4×C5×C7×C9
multiplicative(ℤ/17081)ˣ, (ℤ/17501)ˣ, (ℤ/17537)ˣ, (ℤ/18161)ˣ, (ℤ/18389)ˣ, (ℤ/19685)ˣ, (ℤ/19943)ˣ, (ℤ/20045)ˣ, (ℤ/20425)ˣ, (ℤ/22085)ˣ, (ℤ/22225)ˣ, (ℤ/23241)ˣ, (ℤ/23275)ˣ, (ℤ/23349)ˣ, (ℤ/23421)ˣ, (ℤ/23643)ˣ, (ℤ/23997)ˣ, (ℤ/24273)ˣ, (ℤ/24609)ˣ, (ℤ/24921)ˣ, (ℤ/26607)ˣ, (ℤ/28395)ˣ, (ℤ/28485)ˣ, (ℤ/28575)ˣ, (ℤ/29025)ˣ, (ℤ/30988)ˣ, (ℤ/31132)ˣ, (ℤ/31228)ˣ, (ℤ/31996)ˣ, (ℤ/32812)ˣ, (ℤ/33075)ˣ, (ℤ/34162)ˣ, (ℤ/35002)ˣ, (ℤ/35074)ˣ, (ℤ/35476)ˣ, (ℤ/36322)ˣ, (ℤ/36778)ˣ, (ℤ/39370)ˣ, (ℤ/39886)ˣ, (ℤ/40090)ˣ, (ℤ/40850)ˣ, (ℤ/44170)ˣ, (ℤ/44450)ˣ, (ℤ/45468)ˣ, (ℤ/46482)ˣ, (ℤ/46550)ˣ, (ℤ/46698)ˣ, (ℤ/46842)ˣ, (ℤ/47286)ˣ, (ℤ/47994)ˣ, (ℤ/48546)ˣ, (ℤ/49218)ˣ, (ℤ/49842)ˣ, (ℤ/53214)ˣ, (ℤ/56790)ˣ, (ℤ/56970)ˣ, (ℤ/57150)ˣ, (ℤ/58050)ˣ, (ℤ/66150)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C32×C5×C7
socle, prime radicalC23×C32×C5×C7C2×C3
LCSG ▷ C1
UCSC1 ◁ G

1080 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C7×C8×C9, C2×C3×C42×C5×C7×C9, C23×C3×C4×C5×C7×C9
maximal normal subgroup ofC22×C3×C5×C7×C8×C9, C2×C3×C42×C5×C7×C9, C23×C3×C4×C5×C7×C9
maximal quotient ofC22×C3×C5×C7×C8×C9, C2×C3×C42×C5×C7×C9, C23×C3×C4×C5×C7×C9
automorphism group ofC19×C29×C31, C11×C37×C43, C13×C19×C71, …
outer automorphism group ofC19×C29×C31, C11×C37×C43, C13×C19×C71, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.