Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C17×B(4,𝔽2) ⋊ C2 |
| Sylow | C17 ⋊ #3025 |
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|d^2=g,b^a=be,c^a=cf,f^b=fg,e^c=eg,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17188342, #17188344, #17188370, … |
| maximal normal subgroup of | #17188342, #17188344, #17188370, … |
| maximal quotient of | #17006589, #17006591, #17006598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13900);