Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11763760 |
| unambiguous semidirect product | D17⋊#389 |
| Fitting | C2×C4⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#389 |
800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #17957176, #17957178, #17957186, … |
| maximal normal subgroup of | #17957176, #17957178, #17957186, … |
| maximal quotient of | C2×#14543961, C2×#14543964, C4×#11763760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20965);