Finite Group DatabasebetaFinite Group Databasebeta| order | 24072 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14848 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C17×C59 |
| multiplicative | (ℤ/28091)ˣ, (ℤ/36111)ˣ, (ℤ/36117)ˣ, (ℤ/48148)ˣ, (ℤ/56182)ˣ, (ℤ/72222)ˣ, (ℤ/72234)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C17×C59 |
| socle, prime radical | C22×C3×C17×C59 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
24072 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.