Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×D4×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1782 |
612 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 86 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|a^2=f,c^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^13,f^b=fg,h^c=h^16,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17949028, #17949045, #17949046, … |
| maximal normal subgroup of | #17949028, #17949045, #17949046, … |
| maximal quotient of | #17952433, #17952441, #17952445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20340);