Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#72231615 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #185340 |
| commutator | C2×M16 | C24×C4 |
| Frattini, cosocle | C2×#131 | C25 |
| prime radical | C2×#10580978 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×#2875 ◁ G | |
| LECS | G ▷ C2×#131 ▷ C2×C4 ▷ C2 ▷ C1 | |
At least 6293 conjugacy classes of subgroups; only the 1960 normal subgroups are shown.
152 conjugacy classes — view the full character table.
| maximal subgroup of | #72257323, C2×#72231730 |
| maximal normal subgroup of | #72257323, C2×#72231730 |
| maximal quotient of | #72307659 |
Past the SmallGroups library coverage — no SmallGroups id.