Finite Group DatabasebetaFinite Group Databasebeta| order | 18432 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 393216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C9×C256 |
| multiplicative | (ℤ/24415)ˣ, (ℤ/28527)ˣ, (ℤ/34695)ˣ, (ℤ/37888)ˣ, (ℤ/38036)ˣ, (ℤ/48830)ˣ, (ℤ/57054)ˣ, (ℤ/69390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C128 | C23×C3 |
| socle, prime radical | C23×C3 | C2×C3×C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
18432 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.