Finite Group DatabasebetaFinite Group Databasebeta| order | 23000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 369600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C23×C125 |
| multiplicative | (ℤ/35391)ˣ, (ℤ/47188)ˣ, (ℤ/70782)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C25 | C23×C5×C23 |
| socle, prime radical | C23×C5×C23 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
23000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.