Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C17×#126 ⋊ C2 |
| Sylow | C17 ⋊ #2723 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=ef,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #17241753, #17241766, #17241870, … |
| maximal normal subgroup of | #17241753, #17241766, #17241870, … |
| maximal quotient of | #16961885, #16962049, #16962064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 11425);