Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C213 |
| direct product | C2×#72264735 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#442 |
| commutator | C2×C8 | C25×C4 |
| Frattini, cosocle | C22×C8 | C26 |
| prime radical | C2×D4×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C4×D4 ◁ C2×D4×#97 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
28280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
218 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72265256 |
| maximal normal subgroup of | C2×#72265256 |
Past the SmallGroups library coverage — no SmallGroups id.