Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ C2×#504 |
368 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 200 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,h^a=h^13,c^b=cg,h^d=h^16,h^e=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17960778, #17960784, #17961968, … |
| maximal normal subgroup of | #17960778, #17960784, #17961968, … |
| maximal quotient of | #17978129, #17978141, #17978142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21475);