Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#72216762 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72213256 |
| commutator | C23×#41 | C23×C4 |
| Frattini, cosocle | C22×#535 | C24 |
| prime radical | C2×#72214173 | C2 |
| LCS | G ▷ C23×#41 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C25×C4 ◁ C23×#3484 ◁ G | |
| LECS | G ▷ C22×#535 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
At least 30748 conjugacy classes of subgroups; only the 915 normal subgroups are shown.
172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72217072 |
| maximal normal subgroup of | C2×#72217072 |
Past the SmallGroups library coverage — no SmallGroups id.