Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#72223652 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #1368 |
| commutator | C16 | C2×C82 |
| Frattini, cosocle | C4×#346 | C23 |
| socle | C23 | #7156 |
| prime radical | C24 | #1383 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C42×C8 ◁ C2×C4×#346 ◁ G | |
| LECS | G ▷ C4×#346 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
1524 conjugacy classes of subgroups.
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72223654, C2×#72223670, C2×C8×#7457 |
| maximal normal subgroup of | C2×#72223654, C2×#72223670, C2×C8×#7457 |
Past the SmallGroups library coverage — no SmallGroups id.