Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 206158430208 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C42×C8 |
| abelian | C22×C3×C4×C5×C8×C16 |
| multiplicative | (ℤ/72488)ˣ, (ℤ/73185)ˣ, (ℤ/77792)ˣ, (ℤ/78064)ˣ, (ℤ/84320)ˣ, (ℤ/91840)ˣ, (ℤ/95200)ˣ, (ℤ/97580)ˣ, (ℤ/99552)ˣ, (ℤ/100368)ˣ, (ℤ/102336)ˣ, (ℤ/108732)ˣ, (ℤ/115680)ˣ, (ℤ/118080)ˣ, (ℤ/122400)ˣ, (ℤ/125460)ˣ, (ℤ/146370)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C8 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C2×C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
74400 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.