Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×D4×#595 |
| Fitting | C4×D4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C42×D4 |
924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊C8×#595, #17951862, #17951868, … |
| maximal normal subgroup of | D4⋊C8×#595, #17951862, #17951868, … |
| maximal quotient of | C4×C22⋊C4×#595, C4×C4⋊C4×#595, C4×#11763757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20944);