Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C17×C22⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ #2814 |
478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^16250 conjugacy classes — view the full character table.
| maximal subgroup of | #17009617, #17009621, #17009647, … |
| maximal normal subgroup of | #17009617, #17009621, #17009647, … |
| maximal quotient of | #16964967, #16965005, #16965016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12521);