Finite Group DatabasebetaFinite Group Databasebeta| order | 8192 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C29×C4 · Schur multiplier (H2) = C245 |
| direct product | C27×#442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C29 | C2×D4 |
| commutator | C4 | C29×C4 |
| Frattini, cosocle | C2×C4 | C210 |
| prime radical | C28×D8 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C29 ◁ C27×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
1325122958 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4096 |
2816 conjugacy classes. The character table is too large to display.
| automorphism group of | #12935, #12936, #12937, … |
Past the SmallGroups library coverage — no SmallGroups id.