Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C17×C4⋊C8 ⋊ C2 |
| Sylow | C17 ⋊ #3035 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,f^c=fg,h^c=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | #16929210, #16929212, #16929217, … |
| maximal normal subgroup of | #16929210, #16929212, #16929217, … |
| maximal quotient of | #17016748, #17016763, #17016774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13967);