Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 402653184 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C3×C42×C5×C64 |
| multiplicative | (ℤ/77200)ˣ, (ℤ/78080)ˣ, (ℤ/83200)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C32 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C22×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8736 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.