Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | C2×#72238016 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #201664 |
| commutator | C22×Q8 | C24×C4 |
| Frattini, cosocle | C22×#41 | C25 |
| prime radical | C2×#6437452 | C2 |
| LCS | G ▷ C22×Q8 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×#41 ▷ C23 ▷ C2 ▷ C1 | |
At least 6346 conjugacy classes of subgroups; only the 1576 normal subgroups are shown.
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72238017, #72341880 |
| maximal normal subgroup of | C2×#72238017, #72341880 |
Past the SmallGroups library coverage — no SmallGroups id.