Finite Group DatabasebetaFinite Group Databasebeta| order | 16500 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C11×C125 |
| multiplicative | (ℤ/16817)ˣ, (ℤ/17273)ˣ, (ℤ/33634)ˣ, (ℤ/34546)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C25 | C22×C3×C5×C11 |
| socle, prime radical | C22×C3×C5×C11 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
80 conjugacy classes of subgroups.
16500 conjugacy classes. The character table is too large to display.
| automorphism group of | C67×C251, C23×C751 |
| outer automorphism group of | C67×C251, C23×C751 |
Past the SmallGroups library coverage — no SmallGroups id.