Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#387 ⋊ C2 |
| Sylow | C17 ⋊ C4×#123 |
688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,c^2=e,d^2=g,b^a=be,c^a=cf,h^b=h^16,h^d=h^16280 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#123×D17, C2×#14531305, #17192785, … |
| maximal normal subgroup of | C4×#123×D17, C2×#14531305, #17192785, … |
| maximal quotient of | #16955470, #16955477, #16955479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7031);