Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#72215603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #394066 |
| commutator, Frattini, cosocle | C23×#41 | C25 |
| LCS | G ▷ C23×#41 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C24×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C23×#41 ▷ C23 ▷ C2 ▷ C1 | |
Only the 1867 normal subgroups are shown; non-normal subgroups are omitted.
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72217072 |
| maximal normal subgroup of | C2×#72217072 |
| automorphism group of | C3×#498 |
Past the SmallGroups library coverage — no SmallGroups id.