Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C71 ⋊ C2 |
| Sylow | C71 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 568 |
Polycyclic presentation:
2^5,71|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^70,d^b=de361 conjugacy classes — view the full character table.
| maximal subgroup of | #17986165, #17986166, #17986170, … |
| maximal normal subgroup of | #17986165, #17986166, #17986170, … |
| maximal quotient of | #17985998, #17986004, #17986039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 172);