Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#472 ⋊ C2 |
| Sylow | C17 ⋊ #3067 |
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^16,f^c=fg,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17188275, #17188277, #17188286, … |
| maximal normal subgroup of | #17188275, #17188277, #17188286, … |
| maximal quotient of | #17016564, #17016596, #17016629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14228);