Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,ℤ/8)×#595 |
| Fitting | C17×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C17 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #453×#595, #454×#595, #17971218, … |
| maximal normal subgroup of | #453×#595, #454×#595, #17971218, … |
| maximal quotient of | AGL(1,ℤ/8)×#3624, #17966615, #17966616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21265);