Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C28×C4 · Schur multiplier (H2) = C236 |
| direct product | C27×#106 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C29 | D4 |
| commutator | C4 | C28×C4 |
| Frattini, cosocle | C2×C4 | C29 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C29 ◁ C28×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
46838779 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4096 |
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C27×#442 |
| maximal normal subgroup of | C27×#442 |
Past the SmallGroups library coverage — no SmallGroups id.