Finite Group DatabasebetaFinite Group Databasebeta| order | 24768 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 37158912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C9×C43 |
| multiplicative | (ℤ/49305)ˣ, (ℤ/51208)ˣ, (ℤ/52592)ˣ, (ℤ/61960)ˣ, (ℤ/65740)ˣ, (ℤ/74352)ˣ, (ℤ/74736)ˣ, (ℤ/76812)ˣ, (ℤ/92940)ˣ, (ℤ/93420)ˣ, (ℤ/98610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C24×C3×C43 |
| socle, prime radical | C24×C3×C43 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1494 conjugacy classes of subgroups.
24768 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.