Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×C4⋊C8 ⋊ C4 |
| Sylow | C17 ⋊ #1286 |
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 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=d,b^2=e,c^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^4,d^b=dg,h^b=h^13,h^d=h^16,h^e=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543639, #17950810, #17950815, … |
| maximal normal subgroup of | C2×#14543639, #17950810, #17950815, … |
| maximal quotient of | #17948237, #17948248, #17948252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19365);