Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3461 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^16364 conjugacy classes — view the full character table.
| maximal subgroup of | #16925736, #16925739, #17000909, … |
| maximal normal subgroup of | #16925736, #16925739, #17000909, … |
| maximal quotient of | #17193015, #17193023, #17193031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17937);