Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C4 · Schur multiplier (H2) = C229 |
| direct product | C26×#102 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C28 | D4 |
| commutator | C4 | C27×C4 |
| Frattini, cosocle | C2×C4 | C28 |
| prime radical | C27×D4 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ C27×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
9601832 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1024 |
896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C26×#442, C27×#102 |
| maximal normal subgroup of | C26×#442, C27×#102 |
| maximal quotient of | C27×#102 |
Past the SmallGroups library coverage — no SmallGroups id.