Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C17×C4⋊C8 ⋊ C2 |
| Sylow | C17 ⋊ #2994 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^b=h^16370 conjugacy classes — view the full character table.
| maximal subgroup of | #17005474, #17005478, #17005511, … |
| maximal normal subgroup of | #17005474, #17005478, #17005511, … |
| maximal quotient of | #17033128, #17033175, #17033232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13666);