Finite Group DatabasebetaFinite Group Databasebeta| order | 24192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 995328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C7×C9×C32 |
| multiplicative | (ℤ/36957)ˣ, (ℤ/38361)ˣ, (ℤ/42357)ˣ, (ℤ/49276)ˣ, (ℤ/51148)ˣ, (ℤ/56476)ˣ, (ℤ/72612)ˣ, (ℤ/72684)ˣ, (ℤ/73914)ˣ, (ℤ/76722)ˣ, (ℤ/84714)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C16 | C23×C32×C7 |
| socle, prime radical | C23×C32×C7 | C3×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1200 conjugacy classes of subgroups.
24192 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.