Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C217 |
| direct product | C22×B(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #245225 |
| commutator, Frattini, cosocle | C23×D4 | C26 |
| LCS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
Only the 5339 normal subgroups are shown; non-normal subgroups are omitted.
244 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72209832 |
Past the SmallGroups library coverage — no SmallGroups id.