Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C22⋊Dic19)⋊C3 |
| Hall | C22⋊Dic19 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C22⋊C4 |
| Sylow | C19 ⋊ C3×C22⋊C4 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^2,3,2^2,19|a^2=d,b^a=be,f^a=f^18,f^c=f^754 conjugacy classes — view the full character table.
| maximal subgroup of | #10597263⋊C3, #10597291⋊C3, #10597323⋊C3, … |
| maximal normal subgroup of | #10597263⋊C3, #10597291⋊C3, #10597323⋊C3, … |
| maximal quotient of | (C22⋊(C19⋊C8))⋊C3, (C19⋊C3)⋊#95, #10597291⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 22);