Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#72210598 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | H(3,ℤ/4) |
| commutator | C2×C8 | C2×C82 |
| Frattini, cosocle | C4×#346 | C23 |
| socle | C23 | #7146 |
| prime radical | C24 | #1376 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C22×C8 ◁ C22×C4×C8 ◁ G | |
| LECS | G ▷ C4×#346 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
1488 conjugacy classes of subgroups.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72210681 |
| maximal normal subgroup of | #72210681 |
| maximal quotient of | C2×#72210605 |
Past the SmallGroups library coverage — no SmallGroups id.