Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C17×#497 ⋊ C2 |
| Sylow | C17 ⋊ #3154 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^16,d^c=dg,h^c=h^16,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3154, C2×#14539259, #17903832, … |
| maximal normal subgroup of | D17×#3154, C2×#14539259, #17903832, … |
| maximal quotient of | #17022162, #17022177, #17022210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14985);