Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | C2×#72231314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#106 |
| commutator | C22×C8 | C24×C4 |
| Frattini, cosocle | C23×C8 | C25 |
| prime radical | C27 | SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26×C4 ◁ C26×C8 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
83440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72231459 |
| maximal normal subgroup of | C2×#72231459 |
Past the SmallGroups library coverage — no SmallGroups id.