Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22⋊Q8×#595 |
| Fitting | C17×C22⋊Q8 ⋊ C4 |
| Sylow | C17 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #328×#595, #17952061, #17952071, … |
| maximal normal subgroup of | #328×#595, #17952061, #17952071, … |
| maximal quotient of | #385×#595, #387×#595, #389×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20976);