Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C42×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1839 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^9,h^f=h^13,h^g=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981073, #17981077, #17981531, … |
| maximal normal subgroup of | #17981073, #17981077, #17981531, … |
| maximal quotient of | #17981684, #17981685, #17981796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21653);