Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4⋊C4×#595 |
| Fitting | C2×C4⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #324×#595, #17951773, #340×#595, … |
| maximal normal subgroup of | #324×#595, #17951773, #340×#595, … |
| maximal quotient of | C2×#95×#595, C4×C4⋊C4×#595, C2×#14543959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20941);