Finite Group DatabasebetaFinite Group Databasebeta| order | 8000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 172032000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C43×C5 |
| abelian | C43×C5×C25 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C5 | C23×C52 |
| socle, prime radical | C23×C52 | C23×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1806 conjugacy classes of subgroups.
8000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C42×C5×C8×C25, C2×C43×C5×C25, C3×C43×C5×C25 |
| maximal normal subgroup of | C42×C5×C8×C25, C2×C43×C5×C25, C3×C43×C5×C25 |
| maximal quotient of | C42×C5×C8×C25, C2×C43×C5×C25, C3×C43×C5×C25 |
Past the SmallGroups library coverage — no SmallGroups id.