Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#11763171 |
| Fitting | C2×C17×C4⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ C2×#489 |
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #16929236, #16929242, #16935618, … |
| maximal normal subgroup of | #16929236, #16929242, #16935618, … |
| maximal quotient of | C2×#14528919, C2×#14529473, C2×#14529480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14841);