Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D55 |
| Fitting | C2×C5×D4×C11 ⋊ C2 |
| Hall | C5×C11 ⋊ C22×D4 |
| Sylow | C11 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×D4×D11 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D55 |
| commutator, cosocle | C2×C5×C11 | C24 |
| Frattini | C2 | C23×D55 |
| Fitting | C2×C5×D4×C11 | C2 |
| socle | C22×C5×C11 | C23 |
| hypercenter | C2×D4 | D55 |
| hypocenter | C5×C11 | C22×D4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
472 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 440 |
290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1253);