Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×#595 |
| unambiguous semidirect product | D17⋊(C4×D8) |
| Fitting | C2×D8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 178 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 | #357×#595, #17960901, #361×#595, … |
| maximal normal subgroup of | #357×#595, #17960901, #361×#595, … |
| maximal quotient of | C2×D8×#3624, C2×#14544364, D8×#63242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21257);