Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D277 |
| Fitting | C4⋊Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #332×D277, #333×D277, #47981837, … |
| maximal normal subgroup of | #332×D277, #333×D277, #47981837, … |
| maximal quotient of | #384×D277, #389×D277, #391×D277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1090);