Finite Group DatabasebetaFinite Group Databasebeta| order | 16416 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 310542336 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C33×C4 |
| abelian | C2×C33×C42×C19 |
| multiplicative | (ℤ/20839)ˣ, (ℤ/26793)ˣ, (ℤ/41678)ˣ, (ℤ/53586)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C33×C19 |
| socle, prime radical | C23×C33×C19 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3024 conjugacy classes of subgroups.
16416 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C13×C229 |
| outer automorphism group of | C7×C13×C229 |
Past the SmallGroups library coverage — no SmallGroups id.