Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×C4⋊Q8 ⋊ C4 |
| Sylow | C17 ⋊ #1409 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=g,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^13,c^b=cfg,d^b=def,e^b=eg,d^c=dfg,e^d=eg,h^d=h^1673 conjugacy classes — view the full character table.
| maximal subgroup of | #17949564, #17949565, #17949566, … |
| maximal normal subgroup of | #17949564, #17949565, #17949566, … |
| maximal quotient of | #17949151, #17949188, #17949257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19643);