Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C217 |
| direct product | C2×#72231459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#442 |
| commutator | C22×C8 | C25×C4 |
| Frattini, cosocle | C23×C8 | C26 |
| prime radical | C2×#72231322 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26×C4 ◁ C25×#97 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
Only the 13883 normal subgroups are shown; non-normal subgroups are omitted.
448 conjugacy classes. The character table is too large to display.
| automorphism group of | #12044, #12045, #12085, … |
Past the SmallGroups library coverage — no SmallGroups id.