Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#72241392 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #150393 |
| commutator | #379 | C23×C4 |
| Frattini, cosocle | #1781 | C24 |
| prime radical | C2×#251855 | C2 |
| LCS | G ▷ #379 ▷ C25 ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23 ◁ C25 ◁ C24×D4 ◁ C2×#20586 ◁ G | |
| LECS | G ▷ #1781 ▷ C25 ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
9266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | #72340395, #72340458, #72340478 |
| maximal normal subgroup of | #72340395, #72340458, #72340478 |
Past the SmallGroups library coverage — no SmallGroups id.