Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C17×#135 ⋊ C2 |
| Sylow | C17 ⋊ #3282 |
504 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,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^16,e^d=eg259 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3282, C2×#14540485, #135×C22⋊D17, … |
| maximal normal subgroup of | D17×#3282, C2×#14540485, #135×C22⋊D17, … |
| maximal quotient of | #17024152, #17024167, #17024182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16211);