Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic57 |
| Hall | C3×C19 ⋊ C4⋊C4 |
| Sylow | C19 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C4⋊Dic19 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 912 |
Polycyclic presentation:
2^4,3,19|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^18234 conjugacy classes — view the full character table.
| maximal subgroup of | #14268855, #14268857, #14268861, … |
| maximal normal subgroup of | #14268855, #14268857, #14268861, … |
| maximal quotient of | C4⋊(C3⋊(C19⋊C8)), #14269010, #14269011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 99);