Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#117 ⋊ C4 |
| Sylow | C17 ⋊ #2296 |
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 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|a^2=g,b^2=g,d^2=f,b^a=be,c^a=cf,h^a=h^4,h^b=h^13,h^g=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17957172, #17957174, #17957191, … |
| maximal normal subgroup of | #17957172, #17957174, #17957191, … |
| maximal quotient of | #17962930, #17962937, C4×#11763756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20970);