Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q16×D68 |
| Fitting | C4×Q16×C17 ⋊ C2 |
| Sylow | C17 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
259 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16947761, #16947765, #16947789, … |
| maximal normal subgroup of | #16947761, #16947765, #16947789, … |
| maximal quotient of | #17024516, #17024531, #17024546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16261);