Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | (C2×#3633)⋊Q8 |
| Fitting | C2×Q8×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1984 |
292 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 91 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=f,b^2=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^8,h^b=h^9,h^f=h^13,h^g=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | #17981318, #17981649, #17981694, … |
| maximal normal subgroup of | #17981318, #17981649, #17981694, … |
| maximal quotient of | #17981782, #17981783, #17981784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21661);