Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #2016 |
370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^16,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg256 conjugacy classes — view the full character table.
| maximal subgroup of | #16923144, #16923145, #16923151, … |
| maximal normal subgroup of | #16923144, #16923145, #16923151, … |
| maximal quotient of | #16934821, #16934835, #16934883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5610);