Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 25165824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C5×C128 |
| multiplicative | (ℤ/66664)ˣ, (ℤ/67305)ˣ, (ℤ/71792)ˣ, (ℤ/73216)ˣ, (ℤ/79360)ˣ, (ℤ/89600)ˣ, (ℤ/89740)ˣ, (ℤ/92304)ˣ, (ℤ/93696)ˣ, (ℤ/99996)ˣ, (ℤ/115200)ˣ, (ℤ/115380)ˣ, (ℤ/134610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C64 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C2×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3616 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.