Finite Group DatabasebetaFinite Group Databasebeta| order | 17388 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 85536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C7×C9×C23 |
| multiplicative | (ℤ/17653)ˣ, (ℤ/18373)ˣ, (ℤ/26109)ˣ, (ℤ/35306)ˣ, (ℤ/36746)ˣ, (ℤ/52218)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C7×C23 |
| socle, prime radical | C22×C32×C7×C23 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
200 conjugacy classes of subgroups.
17388 conjugacy classes. The character table is too large to display.
| automorphism group of | C127×C139, C19×C967 |
| outer automorphism group of | C127×C139, C19×C967 |
Past the SmallGroups library coverage — no SmallGroups id.