Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#548 ⋊ C2 |
| Sylow | C17 ⋊ #3275 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^16,c^b=cg,d^b=de,e^b=eg,e^d=eg,h^d=h^16229 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3275, C2×#14540416, #17909503, … |
| maximal normal subgroup of | D17×#3275, C2×#14540416, #17909503, … |
| maximal quotient of | #17025623, #17025714, #17025729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16142);