Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C17 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^7,17|b^a=bd,c^a=ce,f^a=fg,h^a=h^16,e^b=efg,d^c=df,h^c=h^16,e^d=eg124 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2196, C2×#14530769, #17188344, … |
| maximal normal subgroup of | D17×#2196, C2×#14530769, #17188344, … |
| maximal quotient of | #16946354, #16946355, #16946388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6495);