Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of (C11⋊C5)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×(C11⋊C5)⋊Q8 |
| unambiguous semidirect product | (C2×C11⋊C5)⋊Q8 |
| unambiguous semidirect product | (C2×Dic22)⋊C5 |
| Hall | C2×Dic22 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×Q8 |
| Sylow | C11 ⋊ C2×C5×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #66874⋊C5, #66880⋊C5, #66888⋊C5, … |
| maximal normal subgroup of | #66874⋊C5, #66880⋊C5, #66888⋊C5, … |
| maximal quotient of | C4×(C11⋊C5)⋊Q8, #66922⋊C5, #66923⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 114);