Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6442450944 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C42×C16 |
| abelian | C2×C3×C4×C5×C162 |
| multiplicative | (ℤ/61455)ˣ, (ℤ/65552)ˣ, (ℤ/66368)ˣ, (ℤ/77120)ˣ, (ℤ/81940)ˣ, (ℤ/122910)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C82 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C2×C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18976 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.