Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C17×M32 ⋊ C2 |
| Sylow | C17 ⋊ #2112 |
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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|a^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^b=h^16376 conjugacy classes — view the full character table.
| maximal subgroup of | #16921666, #16949381, #16949383, … |
| maximal normal subgroup of | #16921666, #16949381, #16949383, … |
| maximal quotient of | #16943385, #16943457, #16943524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6120);