Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×(C2×#595)⋊Q8 |
| unambiguous semidirect product | D17⋊#391 |
| Fitting | C22×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#391 |
928 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #17956781, #17956782, #17957310, … |
| maximal normal subgroup of | #17956781, #17956782, #17957310, … |
| maximal quotient of | C2×#14543961, C2×#14543963, C4×(C2×#595)⋊Q8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20968);