Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1364 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^16,c^b=cf,d^b=def,f^b=fg,h^b=h^16253 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1364, C2×#14526840, #16945610, … |
| maximal normal subgroup of | D17×#1364, C2×#14526840, #16945610, … |
| maximal quotient of | #16921113, #16921511, #16921976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2566);