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C22×C3×C4×C5×C9×C11 #72201083

order23760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 829440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C4×C5×C9×C11
multiplicative(ℤ/26381)ˣ, (ℤ/26657)ˣ, (ℤ/27269)ˣ, (ℤ/28457)ˣ, (ℤ/29141)ˣ, (ℤ/29887)ˣ, (ℤ/30569)ˣ, (ℤ/30845)ˣ, (ℤ/31339)ˣ, (ℤ/31445)ˣ, (ℤ/31825)ˣ, (ℤ/34685)ˣ, (ℤ/34825)ˣ, (ℤ/36381)ˣ, (ℤ/36417)ˣ, (ℤ/36741)ˣ, (ℤ/36921)ˣ, (ℤ/37467)ˣ, (ℤ/37677)ˣ, (ℤ/37881)ˣ, (ℤ/38649)ˣ, (ℤ/39303)ˣ, (ℤ/40293)ˣ, (ℤ/42471)ˣ, (ℤ/44595)ˣ, (ℤ/44685)ˣ, (ℤ/44775)ˣ, (ℤ/45225)ˣ, (ℤ/48508)ˣ, (ℤ/48556)ˣ, (ℤ/48988)ˣ, (ℤ/49228)ˣ, (ℤ/50236)ˣ, (ℤ/51532)ˣ, (ℤ/52762)ˣ, (ℤ/53314)ˣ, (ℤ/54538)ˣ, (ℤ/56914)ˣ, (ℤ/58282)ˣ, (ℤ/59774)ˣ, (ℤ/61138)ˣ, (ℤ/61690)ˣ, (ℤ/62678)ˣ, (ℤ/62890)ˣ, (ℤ/63650)ˣ, (ℤ/69370)ˣ, (ℤ/69650)ˣ, (ℤ/71388)ˣ, (ℤ/72762)ˣ, (ℤ/72834)ˣ, (ℤ/73482)ˣ, (ℤ/73842)ˣ, (ℤ/74934)ˣ, (ℤ/75354)ˣ, (ℤ/75762)ˣ, (ℤ/77298)ˣ, (ℤ/78606)ˣ, (ℤ/80586)ˣ, (ℤ/84942)ˣ, (ℤ/89190)ˣ, (ℤ/89370)ˣ, (ℤ/89550)ˣ, (ℤ/90450)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C32×C5×C11
socle, prime radicalC23×C32×C5×C11C2×C3
LCSG ▷ C1
UCSC1 ◁ G

1080 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

23760 conjugacy classes. The character table is too large to display.

Relationships

automorphism group ofC23×C31×C37, C19×C23×C61
outer automorphism group ofC23×C31×C37, C19×C23×C61

GAP

Past the SmallGroups library coverage — no SmallGroups id.