Finite Group DatabasebetaFinite Group Databasebeta| order | 29280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10321920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C5×C61 |
| multiplicative | (ℤ/60555)ˣ, (ℤ/64504)ˣ, (ℤ/64592)ˣ, (ℤ/73240)ˣ, (ℤ/73400)ˣ, (ℤ/80740)ˣ, (ℤ/87888)ˣ, (ℤ/89304)ˣ, (ℤ/96756)ˣ, (ℤ/109860)ˣ, (ℤ/110100)ˣ, (ℤ/121110)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C5×C61 |
| socle, prime radical | C24×C3×C5×C61 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
29280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.