Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #1823 |
344 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,e^c=eg,h^c=h^16262 conjugacy classes — view the full character table.
| maximal subgroup of | #16925989, #16925993, #16926019, … |
| maximal normal subgroup of | #16925989, #16925993, #16926019, … |
| maximal quotient of | #16927669, #16927682, #16927695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4594);