Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C42×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4⋊#95 |
656 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 206 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=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^a=h^13,h^f=h^16184 conjugacy classes — view the full character table.
| maximal subgroup of | #17948256, #17948292, #17948294, … |
| maximal normal subgroup of | #17948256, #17948292, #17948294, … |
| maximal quotient of | #17949631, #17949635, #17957021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19688);