Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×Dic277 |
| Sylow | C277 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982958, #100×Dic277, #47982962, … |
| maximal normal subgroup of | #47982958, #100×Dic277, #47982962, … |
| maximal quotient of | M16×#14555660, #47981448, #47981454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 500);