Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#17984552 |
| Fitting | C22×C8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
4444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983500, #47983502, #47983521, … |
| maximal normal subgroup of | #47983500, #47983502, #47983521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1323);