Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#492 ⋊ C2 |
| Sylow | C17 ⋊ #3174 |
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^16,h^d=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | #16945848, D17×#3174, C2×#14539409, … |
| maximal normal subgroup of | #16945848, D17×#3174, C2×#14539409, … |
| maximal quotient of | #17034888, #17038584, #17038701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15135);