Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220×C4 |
| direct product | C2×#117×#120 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C25 |
| commutator | C23 | C26×C4 |
| Frattini, cosocle | C24 | C27 |
| prime radical | C24×#120 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
728676 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#120×#525 |
| maximal normal subgroup of | C2×#120×#525 |
Past the SmallGroups library coverage — no SmallGroups id.