Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×(C2×#595)⋊C4 |
| Fitting | C2×C42×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4×#95 |
752 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #17948235, #17948262, #17948264, … |
| maximal normal subgroup of | #17948235, #17948262, #17948264, … |
| maximal quotient of | (C2×#595)⋊#95, #17949631, C4×#11763674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19682);