Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1319 |
134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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=d,b^2=g,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^9,c^b=cg,d^b=deg,d^c=dg,h^d=h^13,h^f=h^1646 conjugacy classes — view the full character table.
| maximal subgroup of | #17981368, #17981416, C2×#14545812, … |
| maximal normal subgroup of | #17981368, #17981416, C2×#14545812, … |
| maximal quotient of | #17981101, #17981102, #17981109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21538);