Finite Group DatabasebetaFinite Group Databasebeta| order | 26880 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6088116142080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C214×C4 |
| abelian | C24×C3×C42×C5×C7 |
| multiplicative | (ℤ/89320)ˣ, (ℤ/99528)ˣ, (ℤ/107184)ˣ, (ℤ/107880)ˣ, (ℤ/110760)ˣ, (ℤ/113520)ˣ, (ℤ/114840)ˣ, (ℤ/119280)ˣ, (ℤ/121800)ˣ, (ℤ/129360)ˣ, (ℤ/133980)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C26×C3×C5×C7 |
| socle, prime radical | C26×C3×C5×C7 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96120 conjugacy classes of subgroups.
26880 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.