Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×Q8×#595 |
| Fitting | C4×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C42×Q8 |
684 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 320 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊C8×#595, #17951865, #17951871, … |
| maximal normal subgroup of | Q8⋊C8×#595, #17951865, #17951871, … |
| maximal quotient of | C4×C4⋊C4×#595, C4×#11763758, #387×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20945);