Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1374 |
160 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 65 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=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^a=h^9,h^b=h^4,h^d=h^13,h^e=h^16,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981159, #17981160, #17981171, … |
| maximal normal subgroup of | #17981159, #17981160, #17981171, … |
| maximal quotient of | #17981196, #17981210, #17981216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21581);