Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1924 |
280 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 80 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=f,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^4,c^b=cg,h^b=h^13,h^c=h^16,h^f=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | D17⋊#1924, C2×#14544860, #17970191, … |
| maximal normal subgroup of | D17⋊#1924, C2×#14544860, #17970191, … |
| maximal quotient of | #17955687, #17955691, #17955695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20586);