Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64525⋊C3 |
| Fitting | D4×C19 ⋊ C2×C3 |
| Hall | #64525 ⋊ C3 |
| Hall | C19⋊C3 ⋊ D8 |
| Sylow | C19 ⋊ C3×D8 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^2,3,2^2,19|d^2=e,b^a=bd,d^a=de,f^a=f^18,d^b=de,f^c=f^736 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D19⋊C3, #10597357⋊C3, #10597360⋊C3, … |
| maximal normal subgroup of | D8×D19⋊C3, #10597357⋊C3, #10597360⋊C3, … |
| maximal quotient of | #10597264⋊C3, #10597266⋊C3, #10597283⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 18);