Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×#72213022 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | #376 |
| commutator | C42 | C2×C43 |
| Frattini, cosocle | C22×C4×C8 | C24 |
| socle | C23 | #10693 |
| prime radical | C25 | #407 |
| LCS | G ▷ C42 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C22×C4×#97 ◁ G | |
| LECS | G ▷ C22×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
8724 conjugacy classes of subgroups.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72213065, C2×#72213062, #72216679, … |
| maximal normal subgroup of | #72213065, C2×#72213062, #72216679, … |
Past the SmallGroups library coverage — no SmallGroups id.