Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C17×#413 ⋊ C2 |
| Sylow | C17 ⋊ #3018 |
724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^16,e^b=eg,f^b=fg,h^b=h^16,e^c=eg208 conjugacy classes — view the full character table.
| maximal subgroup of | #16951645, #16951650, #16951655, … |
| maximal normal subgroup of | #16951645, #16951650, #16951655, … |
| maximal quotient of | #17006434, #17006485, #17006536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13863);