Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C179 ⋊ C2 |
| Sylow | C179 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,179|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^178,d^b=de901 conjugacy classes — view the full character table.
| maximal subgroup of | #26038605, #26038606, #26038610, … |
| maximal normal subgroup of | #26038605, #26038606, #26038610, … |
| maximal quotient of | #26038438, #26038444, #26038479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 172);