Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C17×#97 ⋊ C4 |
| Sylow | C17 ⋊ #1726 |
328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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=f,d^2=g,h^a=h^4,c^b=cg,h^b=h^13,h^d=h^16,h^e=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17952189, #17952193, #17952205, … |
| maximal normal subgroup of | #17952189, #17952193, #17952205, … |
| maximal quotient of | #97×#3624, #17950267, #17950272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20168);