Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #1783 |
820 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^13,f^b=fg,h^c=h^16,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17949025, #17949041, #17949049, … |
| maximal normal subgroup of | #17949025, #17949041, #17949049, … |
| maximal quotient of | #17952427, #17952441, #17952442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20343);