Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of (C11⋊C5)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊AGL(1,𝔽11) |
| unambiguous semidirect product | C23⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C2×C22⋊D11)⋊C5 |
| Fitting | C23×C11 ⋊ C2×C5 |
| Hall | C2×C22⋊D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D4 |
| Sylow | C11 ⋊ C2×C5×D4 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #66870⋊C5, #66938⋊C5, ((C22⋊D11)⋊C4)⋊C5, … |
| maximal normal subgroup of | #66870⋊C5, #66938⋊C5, ((C22⋊D11)⋊C4)⋊C5, … |
| maximal quotient of | C2×(Dic11⋊C4)⋊C5, #66977⋊C5, C2×((C2×D11)⋊C4)⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 123);