Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×#72216466 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72216464 |
| commutator, Frattini, cosocle | C2×#379 | C25 |
| LCS | G ▷ C2×#379 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C26 ◁ C22×#2846 ◁ G | |
| LECS | G ▷ C2×#379 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
At least 10848 conjugacy classes of subgroups; only the 1019 normal subgroups are shown.
154 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.