Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C17×#493 ⋊ C2 |
| Sylow | C17 ⋊ #3155 |
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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|b^2=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^d=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | #17188634, #17188652, #17188670, … |
| maximal normal subgroup of | #17188634, #17188652, #17188670, … |
| maximal quotient of | #17022186, #17022226, #17022252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14990);