Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | D17⋊#433 |
| Sylow | C17 ⋊ C2×#433 |
412 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 162 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|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^13,c^b=cg,h^d=h^16,h^f=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #433×#595, #17968646, #17968659, … |
| maximal normal subgroup of | #433×#595, #17968646, #17968659, … |
| maximal quotient of | #17968246, #17968276, #17968492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21184);