Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1288 |
152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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|a^2=d,b^2=e,c^2=fg,e^2=g,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1288, C2×#14526648, #16924166, … |
| maximal normal subgroup of | D17×#1288, C2×#14526648, #16924166, … |
| maximal quotient of | #16920859, #16920869, #16920874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2374);