Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#10587465 |
| Sylow | C17 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^16592 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#10587465, #16921763, #16921765, … |
| maximal normal subgroup of | D4⋊#10587465, #16921763, #16921765, … |
| maximal quotient of | #16921990, #16921997, #16922011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2706);