Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C17×#123 ⋊ C2 |
| Sylow | C17 ⋊ #2849 |
1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|c^2=e,b^a=be,c^a=cf,d^a=dg,h^d=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | #17065908, #17065910, #17065921, … |
| maximal normal subgroup of | #17065908, #17065910, #17065921, … |
| maximal quotient of | #16965485, #16965531, #16965536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12799);