Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×#107 ⋊ C4 |
| Sylow | C17 ⋊ #1386 |
140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 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=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,c^b=cg,h^b=h^13,h^e=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543855, #17960537, #17960540, … |
| maximal normal subgroup of | C2×#14543855, #17960537, #17960540, … |
| maximal quotient of | #17948549, #17948609, #17948620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19581);