Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#134033 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #1781 |
| commutator | C25 | C24×C4 |
| Frattini, cosocle | C22×C22⋊C4 | C25 |
| prime radical | C23×#2846 | C2 |
| LCS | G ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26 ◁ C24×#120 ◁ G | |
| LECS | G ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
2156844 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213827 |
| maximal normal subgroup of | C22×#72213827 |
Past the SmallGroups library coverage — no SmallGroups id.