Finite Group DatabasebetaFinite Group Databasebeta| order | 16000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6606028800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4 |
| abelian | C23×C42×C125 |
| multiplicative | (ℤ/60240)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C25 | C25×C5 |
| socle, prime radical | C25×C5 | C22×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6000 conjugacy classes of subgroups.
16000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×C4×C8×C125, C22×C43×C125, C24×C42×C125 |
| maximal normal subgroup of | C23×C4×C8×C125, C22×C43×C125, C24×C42×C125 |
| maximal quotient of | C23×C4×C8×C125, C22×C43×C125, C24×C42×C125 |
Past the SmallGroups library coverage — no SmallGroups id.