Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊(C23⋊C8) |
| Sylow | C23 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^22,c^b=ce248 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D4⋊C8, C2×D4⋊(C23⋊C8), #15671776, … |
| maximal normal subgroup of | D23×D4⋊C8, C2×D4⋊(C23⋊C8), #15671776, … |
| maximal quotient of | #15671218, #15671220, #15671238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 277);