Finite Group DatabasebetaFinite Group Databasebeta| order | 29280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 61440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C3×C4×C5×C8×C61 |
| multiplicative | (ℤ/30053)ˣ, (ℤ/31733)ˣ, (ℤ/36605)ˣ, (ℤ/60106)ˣ, (ℤ/63466)ˣ, (ℤ/73210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C22×C3×C5×C61 |
| socle, prime radical | C22×C3×C5×C61 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
176 conjugacy classes of subgroups.
29280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.