Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×#595 |
| unambiguous semidirect product | D17⋊(C4×#41) |
| Fitting | C2×#41×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×C4×#41 |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #17956807, #17956810, #17956852, … |
| maximal normal subgroup of | #17956807, #17956810, #17956852, … |
| maximal quotient of | C2×#117×#595, C2×C4×D4×#595, C2×C4×Q8×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21486);