Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 73728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C16×C27 |
| multiplicative | (ℤ/5559)ˣ, (ℤ/6495)ˣ, (ℤ/6885)ˣ, (ℤ/6928)ˣ, (ℤ/6976)ˣ, (ℤ/7412)ˣ, (ℤ/8660)ˣ, (ℤ/11118)ˣ, (ℤ/12990)ˣ, (ℤ/13770)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8×C9 | C23×C3 |
| socle, prime radical | C23×C3 | C2×C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
3456 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.