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 ⋊ #1733 |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^4,c^b=cg,h^b=h^13,h^e=h^16,h^f=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17956749, #17956752, #17956757, … |
| maximal normal subgroup of | #17956749, #17956752, #17956757, … |
| maximal quotient of | #17950373, #17950374, #17950381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20192);