Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #1842 |
300 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 138 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=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^13,h^b=h^16,h^f=h^16184 conjugacy classes — view the full character table.
| maximal subgroup of | #17948273, #17948295, #17948316, … |
| maximal normal subgroup of | #17948273, #17948295, #17948316, … |
| maximal quotient of | #17953810, #17953811, #17953813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20443);