Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #2374 |
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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=g,b^2=g,c^2=ef,d^2=ef,b^a=be,c^a=cf,d^b=de,h^b=h^16,h^c=h^16,h^d=h^16274 conjugacy classes — view the full character table.
| maximal subgroup of | #16951081, #16951085, #16951588, … |
| maximal normal subgroup of | #16951081, #16951085, #16951588, … |
| maximal quotient of | #16955788, #16955878, #16955913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7643);