Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#72213969 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #18524 |
| commutator | C4×C8 | C24×C4 |
| Frattini, cosocle | C2×C4×C8 | C25 |
| prime radical | C22×#12310 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C2×C4×#97 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
14950 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
176 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.