Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C17×#97 ⋊ C2 |
| Sylow | C17 ⋊ #1749 |
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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=f,c^2=e,f^2=g,b^a=bd,h^a=h^16,c^b=cg376 conjugacy classes — view the full character table.
| maximal subgroup of | #16925789, #16925792, #16925795, … |
| maximal normal subgroup of | #16925789, #16925792, #16925795, … |
| maximal quotient of | #16924798, #16924809, #16924835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4273);