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C23×C3×C4×C7×C9 #72185234

order6048
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13934592
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C3×C4×C7×C9
multiplicative(ℤ/11571)ˣ, (ℤ/12255)ˣ, (ℤ/12728)ˣ, (ℤ/13072)ˣ, (ℤ/13208)ˣ, (ℤ/13335)ˣ, (ℤ/13965)ˣ, (ℤ/14224)ˣ, (ℤ/14504)ˣ, (ℤ/14896)ˣ, (ℤ/15428)ˣ, (ℤ/16340)ˣ, (ℤ/17780)ˣ, (ℤ/18288)ˣ, (ℤ/18576)ˣ, (ℤ/18620)ˣ, (ℤ/19092)ˣ, (ℤ/19812)ˣ, (ℤ/19836)ˣ, (ℤ/21168)ˣ, (ℤ/21756)ˣ, (ℤ/21924)ˣ, (ℤ/22860)ˣ, (ℤ/23142)ˣ, (ℤ/23220)ˣ, (ℤ/24510)ˣ, (ℤ/26460)ˣ, (ℤ/26670)ˣ, (ℤ/27930)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C24×C32×C7
socle, prime radicalC24×C32×C7C2×C3
LCSG ▷ C1
UCSC1 ◁ G

2360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C7×C8×C9, C22×C3×C42×C7×C9, C24×C3×C4×C7×C9, …
maximal normal subgroup ofC23×C3×C7×C8×C9, C22×C3×C42×C7×C9, C24×C3×C4×C7×C9, …
maximal quotient ofC23×C3×C7×C8×C9, C22×C3×C42×C7×C9, C24×C3×C4×C7×C9, …
automorphism group ofC8×C37×C43, C16×C19×C43, C8×C13×C127, …
outer automorphism group ofC8×C37×C43, C16×C19×C43, C8×C13×C127, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.