Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#22579805 |
| Sylow | C277 ⋊ C2×#103 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
4444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982986, C4×#22579805, #47982996, … |
| maximal normal subgroup of | #47982986, C4×#22579805, #47982996, … |
| maximal quotient of | C2×#31799734, #47981571, #47981597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 541);