Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#72216682 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72216681 |
| commutator | C27 | C23×C4 |
| Frattini, cosocle | C2×#2846 | C24 |
| prime radical | C2×#72209716 | C2 |
| LCS | G ▷ C27 ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C26 ◁ C22×#2846 ◁ G | |
| LECS | G ▷ C2×#2846 ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
At least 13227 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
142 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216741 |
| maximal normal subgroup of | C2×#72216741 |
Past the SmallGroups library coverage — no SmallGroups id.