Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#471 ⋊ C2 |
| Sylow | C17 ⋊ #3069 |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,f^c=fg,h^d=h^16157 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3069, C2×#14538516, #17901742, … |
| maximal normal subgroup of | D17×#3069, C2×#14538516, #17901742, … |
| maximal quotient of | #17017096, #17017098, #17017107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14242);