Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#72215520 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#2668 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 8900 conjugacy classes of subgroups; only the 5136 normal subgroups are shown.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216359, D3×#72215520 |
| maximal normal subgroup of | C2×#72216359 |
| maximal quotient of | D3×#72215520 |
| automorphism group of | C3×#499 |
Past the SmallGroups library coverage — no SmallGroups id.