Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×Q8×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1461 |
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,b^2=f,c^2=fg,e^2=g,b^a=bd,d^a=df,h^a=h^9,e^b=ef,h^c=h^4,h^e=h^13,h^g=h^1664 conjugacy classes — view the full character table.
| maximal subgroup of | #17981318, #101×#3633, #17981649, … |
| maximal normal subgroup of | #17981318, #101×#3633, #17981649, … |
| maximal quotient of | #17981519, #17981521, #17981536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21625);