Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^4,e^b=eg,h^b=h^13,h^c=h^16,h^e=h^16,h^f=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #344×#595, #17956650, #17956770, … |
| maximal normal subgroup of | #344×#595, #17956650, #17956770, … |
| maximal quotient of | #17950586, #17950589, #17950594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20222);