Finite Group DatabasebetaFinite Group Databasebeta| order | 29952 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 147456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C13×C128 |
| multiplicative | (ℤ/34951)ˣ, (ℤ/44937)ˣ, (ℤ/69902)ˣ, (ℤ/89874)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C64 | C22×C32×C13 |
| socle, prime radical | C22×C32×C13 | C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
276 conjugacy classes of subgroups.
29952 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.