Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #107×#595 |
| Fitting | C17×#107 ⋊ C4 |
| Sylow | C17 ⋊ C4×#107 |
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #357×#595, #358×#595, #17960901, … |
| maximal normal subgroup of | #357×#595, #358×#595, #17960901, … |
| maximal quotient of | #335×#595, #17952325, #17952337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20323);