Finite Group DatabasebetaFinite Group Databasebeta| order | 16704 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 24772608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C9×C29 |
| multiplicative | (ℤ/32745)ˣ, (ℤ/34928)ˣ, (ℤ/41840)ˣ, (ℤ/43660)ˣ, (ℤ/65490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C24×C3×C29 |
| socle, prime radical | C24×C3×C29 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1494 conjugacy classes of subgroups.
16704 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.