Finite Group DatabasebetaFinite Group Databasebeta| order | 27960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 311808 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C233 |
| multiplicative | (ℤ/35959)ˣ, (ℤ/43431)ˣ, (ℤ/46167)ˣ, (ℤ/46233)ˣ, (ℤ/55928)ˣ, (ℤ/57908)ˣ, (ℤ/61556)ˣ, (ℤ/71918)ˣ, (ℤ/83892)ˣ, (ℤ/86862)ˣ, (ℤ/92334)ˣ, (ℤ/92466)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
27960 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.