Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#595 |
| unambiguous semidirect product | D17⋊(C4×Q8) |
| Fitting | C2×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #101×#595, #103×#595, #14544557, … |
| maximal normal subgroup of | #101×#595, #103×#595, #14544557, … |
| maximal quotient of | C2×C4⋊C4×#595, C4×Q8×#595, C2×#11763758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1614);