Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6291456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C128 |
| multiplicative | (ℤ/17920)ˣ, (ℤ/19968)ˣ, (ℤ/23040)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C64 | C24×C3 |
| socle, prime radical | C24×C3 | C2×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1808 conjugacy classes of subgroups.
6144 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.