Finite Group DatabasebetaFinite Group Databasebeta| order | 24768 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4128768 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C8×C43 |
| multiplicative | (ℤ/36155)ˣ, (ℤ/40287)ˣ, (ℤ/46485)ˣ, (ℤ/53716)ˣ, (ℤ/72310)ˣ, (ℤ/80574)ˣ, (ℤ/92970)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C32×C43 |
| socle, prime radical | C23×C32×C43 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
972 conjugacy classes of subgroups.
24768 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.