Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#11764308 |
| unambiguous semidirect product | D277⋊(C4×Q8) |
| Fitting | C2×Q8×C277 ⋊ C4 |
| Sylow | C277 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1614);