Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C218 |
| direct product | C2×#72216660 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#120 |
| commutator, Frattini, cosocle | C25 | C26 |
| LCS | G ▷ C25 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
At least 9691 conjugacy classes of subgroups; only the 6656 normal subgroups are shown.
248 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222918 |
| maximal quotient of | C2×#72216662, #72303619, #72339316 |
Past the SmallGroups library coverage — no SmallGroups id.