Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C214 |
| direct product | C2×#72237215 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×#127 |
| commutator, Frattini, cosocle | C24×C4 | C25 |
| socle | C24 | C2×#392 |
| LCS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
At least 8716 conjugacy classes of subgroups; only the 4648 normal subgroups are shown.
248 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72239586 |
| maximal normal subgroup of | C2×#72239586 |
Past the SmallGroups library coverage — no SmallGroups id.