Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| unambiguous semidirect product | #595⋊M32 |
| Sylow | C17 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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=e,d^2=f,f^2=g,c^a=cg,h^a=h^9,h^b=h^4,h^d=h^13,h^e=h^16,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981199, #17981201, #17981203, … |
| maximal normal subgroup of | #17981199, #17981201, #17981203, … |
| maximal quotient of | C8×#10587670, C8×#10587666, #17981831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21670);