Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#72213553 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #1270 |
| commutator | C2×C42 | C23×C8 |
| Frattini, cosocle | #1744 | C24 |
| socle | C23 | C2×#1270 |
| prime radical | C23×#127 | C8 |
| LCS | G ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ C22×#1744 ◁ G | |
| LECS | G ▷ #1744 ▷ C2×C42 ▷ C22 ▷ C1 | |
8828 conjugacy classes of subgroups.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72213854, #72215105, #72216408, … |
| maximal normal subgroup of | #72213854, #72215105, #72216408, … |
Past the SmallGroups library coverage — no SmallGroups id.