Finite Group DatabasebetaFinite Group Databasebeta| order | 16224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3119800320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C25×C3×C169 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C13 | C25×C3×C13 |
| socle, prime radical | C25×C3×C13 | C13 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2244 conjugacy classes of subgroups.
16224 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C3×C4×C169, C26×C3×C169 |
| maximal normal subgroup of | C24×C3×C4×C169, C26×C3×C169 |
| maximal quotient of | C24×C3×C4×C169, C26×C3×C169 |
Past the SmallGroups library coverage — no SmallGroups id.