Finite Group DatabasebetaFinite Group Databasebeta| order | 19712 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 23592960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C7×C11×C16 |
| multiplicative | (ℤ/34017)ˣ, (ℤ/38985)ˣ, (ℤ/41584)ˣ, (ℤ/42688)ˣ, (ℤ/45356)ˣ, (ℤ/51980)ˣ, (ℤ/68034)ˣ, (ℤ/77970)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C24×C7×C11 |
| socle, prime radical | C24×C7×C11 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2044 conjugacy classes of subgroups.
19712 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.