Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×SD16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3043 |
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^16,f^c=fg256 conjugacy classes — view the full character table.
| maximal subgroup of | #17071728, #17071732, #17082195, … |
| maximal normal subgroup of | #17071728, #17071732, #17082195, … |
| maximal quotient of | #17019597, #17019606, #17019615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14028);