Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #124×#595 |
| Fitting | C17×#124 ⋊ C4 |
| Sylow | C17 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #329×#595, #17952094, #17952102, … |
| maximal normal subgroup of | #329×#595, #17952094, #17952102, … |
| maximal quotient of | #388×#595, #390×#595, #391×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20977);