Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C214 |
| direct product | C2×#72216433 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72216432 |
| commutator, Frattini, cosocle | C27 | C25 |
| LCS | G ▷ C27 ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ C28 ◁ G | |
| LECS | G ▷ C27 ▷ C24 ▷ C2 ▷ C1 | |
Only the 1123 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 1123 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
190 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.