Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#11763201 |
| Fitting | C2×C17×C4⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ C2×#497 |
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #16929260, #16935619, #16935620, … |
| maximal normal subgroup of | #16929260, #16935619, #16935620, … |
| maximal quotient of | C2×#14528409, C2×#14528416, C2×#14528428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14948);