Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C17×#124 ⋊ C2 |
| Sylow | C17 ⋊ #2684 |
688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 137 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|b^2=f,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #16953292, #16953294, #16953769, … |
| maximal normal subgroup of | #16953292, #16953294, #16953769, … |
| maximal quotient of | #16961607, #16961714, #16962124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10886);