Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C17×#331 ⋊ C2 |
| Sylow | C17 ⋊ #1701 |
176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=dfg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^16,e^c=eg,h^c=h^16175 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1701, C2×#14528344, #17016901, … |
| maximal normal subgroup of | D17×#1701, C2×#14528344, #17016901, … |
| maximal quotient of | #16927437, #16930534, #16930558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4070);