Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C8 · Schur multiplier (H2) = C214 |
| direct product | C2×#72224948 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#442 |
| commutator | C8 | C25×C8 |
| Frattini, cosocle | C4×C8 | C26 |
| socle | C22 | C22×#1580 |
| prime radical | C2×#62635 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#131 ◁ C2×#33326 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
21938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
356 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72225087, C2×#72225118, C2×#72224969 |
| maximal normal subgroup of | C2×#72225087, C2×#72225118, C2×#72224969 |
| maximal quotient of | #72322318 |
Past the SmallGroups library coverage — no SmallGroups id.