Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#11763752 |
| unambiguous semidirect product | D17⋊#381 |
| Fitting | C23×C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 258 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 | #17950569, #17950572, C2×#14543632, … |
| maximal normal subgroup of | #17950569, #17950572, C2×#14543632, … |
| maximal quotient of | C2×#14543958, C2×#14543960, C4×#11763752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20953);