Finite Group DatabasebetaFinite Group Databasebeta| order | 24480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4718592 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C42×C5×C17 |
| multiplicative | (ℤ/31415)ˣ, (ℤ/33475)ˣ, (ℤ/35735)ˣ, (ℤ/39819)ˣ, (ℤ/45945)ˣ, (ℤ/53092)ˣ, (ℤ/62830)ˣ, (ℤ/66950)ˣ, (ℤ/71470)ˣ, (ℤ/79638)ˣ, (ℤ/91890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C32×C5×C17 |
| socle, prime radical | C23×C32×C5×C17 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
24480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.