Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C42×C17 ⋊ C2 |
| Sylow | C17 ⋊ #1896 |
442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=df,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^16556 conjugacy classes — view the full character table.
| maximal subgroup of | #16925834, #16925836, #16925839, … |
| maximal normal subgroup of | #16925834, #16925836, #16925839, … |
| maximal quotient of | #16929655, #16929660, #16929685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4953);