Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#72231210 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #10965 |
| commutator | C24×C4 | C23×C4 |
| Frattini, cosocle | C22×C4×D4 | C24 |
| prime radical | C2×#649038 | C2 |
| LCS | G ▷ C24×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C23×D42 ◁ G | |
| LECS | G ▷ C22×C4×D4 ▷ C23 ▷ C2 ▷ C1 | |
At least 8633 conjugacy classes of subgroups; only the 872 normal subgroups are shown.
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240196 |
| maximal normal subgroup of | C2×#72240196 |
Past the SmallGroups library coverage — no SmallGroups id.