Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | D4×#21452 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C24×D4 |
| commutator | C22×C4 | C25×C4 |
| Frattini, cosocle | C23×C4 | C26 |
| prime radical | C2×D4×#447 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C22×C42×D4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 9701 conjugacy classes of subgroups; only the 8850 normal subgroups are shown.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72306287 |
| maximal normal subgroup of | #72306287 |
| maximal quotient of | D4×#495725 |
Past the SmallGroups library coverage — no SmallGroups id.