Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×M64 ⋊ C2 |
| Sylow | C17 ⋊ #2264 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^16,d^b=de,e^b=ef,f^b=fg,h^b=h^16346 conjugacy classes — view the full character table.
| maximal subgroup of | #16954941, #16954944, #16955003, … |
| maximal normal subgroup of | #16954941, #16954944, #16955003, … |
| maximal quotient of | #16954764, #16954772, #16954831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6830);