Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C211×C4 |
| direct product | C2×#72317386 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×#99 |
| commutator | C24 | C23×C42 |
| Frattini, cosocle | C22×#41 | C25 |
| socle | C23 | C2×C4×#99 |
| prime radical | C23×#525 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8 ◁ C24×C8 ◁ C24×#131 ◁ G | |
| LECS | G ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1 | |
70472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
320 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.