Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#14555660 |
| Sylow | C277 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981964, SD16×#14555660, #47981971, … |
| maximal normal subgroup of | #47981964, SD16×#14555660, #47981971, … |
| maximal quotient of | C4⋊C4×#14555660, #47983726, #47983886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 675);