Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1290 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^13,d^b=dg,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17948376, #17948377, #17948378, … |
| maximal normal subgroup of | #17948376, #17948377, #17948378, … |
| maximal quotient of | #17948242, #17948250, #17948291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19375);