Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | D4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3298 |
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,d^b=de,f^c=fg235 conjugacy classes — view the full character table.
| maximal subgroup of | #17023830, #17023834, #17023845, … |
| maximal normal subgroup of | #17023830, #17023834, #17023845, … |
| maximal quotient of | D4×#10587506, #17050532, #17051472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16375);