Finite Group DatabasebetaFinite Group Databasebeta| order | 26112 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 100663296 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C8 |
| abelian | C22×C3×C8×C16×C17 |
| multiplicative | (ℤ/48909)ˣ, (ℤ/55624)ˣ, (ℤ/56032)ˣ, (ℤ/61376)ˣ, (ℤ/64736)ˣ, (ℤ/65212)ˣ, (ℤ/78528)ˣ, (ℤ/78912)ˣ, (ℤ/83232)ˣ, (ℤ/83436)ˣ, (ℤ/83844)ˣ, (ℤ/97818)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C24×C3×C17 |
| socle, prime radical | C24×C3×C17 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3848 conjugacy classes of subgroups.
26112 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.