Finite Group DatabasebetaFinite Group Databasebeta| order | 26880 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1572864 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8 |
| abelian | C2×C3×C5×C7×C8×C16 |
| multiplicative | (ℤ/29971)ˣ, (ℤ/32431)ˣ, (ℤ/33439)ˣ, (ℤ/34153)ˣ, (ℤ/41451)ˣ, (ℤ/41697)ˣ, (ℤ/42993)ˣ, (ℤ/55268)ˣ, (ℤ/59942)ˣ, (ℤ/64862)ˣ, (ℤ/66878)ˣ, (ℤ/68306)ˣ, (ℤ/82902)ˣ, (ℤ/83394)ˣ, (ℤ/85986)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C23×C3×C5×C7 |
| socle, prime radical | C23×C3×C5×C7 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1592 conjugacy classes of subgroups.
26880 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.