Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C222 |
| direct product | C2×#72237167 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C24×D4 |
| commutator, Frattini, cosocle | C23×C4 | C27 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C22×C4×#525 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Only the 52283 normal subgroups are shown; non-normal subgroups are omitted.
520 conjugacy classes. The character table is too large to display.
| automorphism group of | #11647, #11648, #11673, … |
Past the SmallGroups library coverage — no SmallGroups id.