Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#10587534 |
| Fitting | C4×C8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4×#107 |
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #17948597, #17948598, #17948618, … |
| maximal normal subgroup of | #17948597, #17948598, #17948618, … |
| maximal quotient of | C4×#11763672, C4×#11763673, #17952323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20322);