Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#451 ⋊ C2 |
| Sylow | C17 ⋊ #3277 |
476 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=g,d^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,h^c=h^16,e^d=eg,h^d=h^16181 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3277, C2×#14540441, #17909497, … |
| maximal normal subgroup of | D17×#3277, C2×#14540441, #17909497, … |
| maximal quotient of | #17025648, #17025761, #17025762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16167);