Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C71 ⋊ C2 |
| Sylow | C71 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^5,71|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^70,d^b=de,f^b=f^70361 conjugacy classes — view the full character table.
| maximal subgroup of | #17986178, #17986179, #17986183, … |
| maximal normal subgroup of | #17986178, #17986179, #17986183, … |
| maximal quotient of | #17986001, #17986009, #17986041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 179);