Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1770 |
272 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^4,c^b=cg,h^c=h^13,h^e=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17951995, #17951996, #17951999, … |
| maximal normal subgroup of | #17951995, #17951996, #17951999, … |
| maximal quotient of | #17952265, #17952271, #17952290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20306);