Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C17×H(5,𝔽2) ⋊ C2 |
| Sylow | C17 ⋊ #3008 |
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^16,e^b=eg,d^c=dg304 conjugacy classes — view the full character table.
| maximal subgroup of | #16951902, #16951904, #16951923, … |
| maximal normal subgroup of | #16951902, #16951904, #16951923, … |
| maximal quotient of | #17007486, #17007574, #17007660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13778);