Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of D5×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D11×#168 |
| derived, Hall | C5×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ C2×#168 |
| Sylow | C5 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D5×D11 |
| commutator, hypocenter | C5×C11 | C2×C8 |
| Fitting, cosocle | C4×C5×C11 | C22 |
| socle | C2×C5×C11 | C2×C4 |
| prime radical | C2×C5×D11 | C4 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#674, #13182573, C8×D5×D11, … |
| maximal normal subgroup of | D11×#674, #13182573, C8×D5×D11, … |
| maximal quotient of | D11×#672, #13182263, #168×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 33);