Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#152018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #12687 |
| commutator | C22×D4 | C24×C4 |
| Frattini, cosocle | C2×#127 | C25 |
| prime radical | C23×#3019 | C2 |
| LCS | G ▷ C22×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C25×C4 ◁ C23×#535 ◁ G | |
| LECS | G ▷ C2×#127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
156240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213671 |
| maximal normal subgroup of | C22×#72213671 |
Past the SmallGroups library coverage — no SmallGroups id.