Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C211×C4 |
| direct product | C2×#72317355 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | #1781 |
| commutator | C22×C4 | C23×C42 |
| Frattini, cosocle | C22×#41 | C25 |
| socle | C22 | C4×#1781 |
| prime radical | C2×#62811 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C23×C8 ◁ C24×#131 ◁ G | |
| LECS | G ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1 | |
62892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72317393 |
| maximal normal subgroup of | C2×#72317393 |
Past the SmallGroups library coverage — no SmallGroups id.