Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #66991⋊C5 |
| Fitting | C2×D4×C11 ⋊ C2×C5 |
| Hall | #66991 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #121 |
| Sylow | C11 ⋊ C5×#121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×AGL(1,𝔽11) |
| commutator, socle, cosocle | C22×C11 | C23×C5 |
| Fitting | C2×D4×C11 | C2×C5 |
| hypercenter | C2×D4 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#121 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
188 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^3,5,2^2,11|b^a=bf,c^a=cf,g^a=g^10,c^b=ce,g^d=g^980 conjugacy classes — view the full character table.
| maximal subgroup of | #72248821, #121×AGL(1,𝔽11), #72248843, … |
| maximal normal subgroup of | #72248821, #121×AGL(1,𝔽11), #72248843, … |
| maximal quotient of | #72254527 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 350);