Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C17×#469 ⋊ C2 |
| Sylow | C17 ⋊ #3058 |
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^16,d^c=dg,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #16945316, #16945324, #17188224, … |
| maximal normal subgroup of | #16945316, #16945324, #17188224, … |
| maximal quotient of | #17017393, #17017432, #17017480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14156);