Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11763057 |
| Fitting | C2×C17×C22⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ C2×#468 |
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #17040950, C4×#11763057, #17040987, … |
| maximal normal subgroup of | #17040950, C4×#11763057, #17040987, … |
| maximal quotient of | C2×#14528251, C2×#14528285, C2×#14528319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14100);