Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C2×D4×#2010 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×#127 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| socle | C23 | C22×#392 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4×D4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 9589 conjugacy classes of subgroups; only the 8032 normal subgroups are shown.
260 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.