Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#446 ⋊ C2 |
| Sylow | C17 ⋊ #3402 |
356 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=e,c^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,c^b=cg,d^b=de,f^c=fg,h^c=h^16253 conjugacy classes — view the full character table.
| maximal subgroup of | #16947893, #16947897, #16947907, … |
| maximal normal subgroup of | #16947893, #16947897, #16947907, … |
| maximal quotient of | #17051197, #17053210, #17054138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17591);