Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3507 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=fg,c^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^16,d^b=df364 conjugacy classes — view the full character table.
| maximal subgroup of | #16925891, #16925895, #16926309, … |
| maximal normal subgroup of | #16925891, #16925895, #16926309, … |
| maximal quotient of | #17194461, #17194689, #17194764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18375);