Finite Group DatabasebetaFinite Group Databasebeta| order | 24288 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 675840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C11×C23 |
| multiplicative | (ℤ/31855)ˣ, (ℤ/34385)ˣ, (ℤ/35455)ˣ, (ℤ/39507)ˣ, (ℤ/45555)ˣ, (ℤ/45585)ˣ, (ℤ/48592)ˣ, (ℤ/52676)ˣ, (ℤ/60740)ˣ, (ℤ/63710)ˣ, (ℤ/68770)ˣ, (ℤ/70910)ˣ, (ℤ/79014)ˣ, (ℤ/91110)ˣ, (ℤ/91170)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C11×C23 |
| socle, prime radical | C23×C3×C11×C23 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
24288 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.