Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | #442×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×D4×#120 |
| commutator | C23×C4 | C25×C4 |
| Frattini, cosocle | C24×C4 | C26 |
| prime radical | C2×D8×B(4,𝔽2) | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
Only the 8733 normal subgroups are shown; non-normal subgroups are omitted.
352 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.