Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5637144576 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4 |
| abelian | C23×C3×C4×C5×C64 |
| multiplicative | (ℤ/84920)ˣ, (ℤ/98560)ˣ, (ℤ/101904)ˣ, (ℤ/109824)ˣ, (ℤ/115800)ˣ, (ℤ/119040)ˣ, (ℤ/126720)ˣ, (ℤ/127380)ˣ, (ℤ/134400)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
19104 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.