Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #64515⋊C3 |
| Fitting | C8×C19 ⋊ C2×C3 |
| Hall | #64515 ⋊ C3 |
| Hall | C19⋊C3 ⋊ M16 |
| Sylow | C19 ⋊ C3×M16 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^2,3,2^2,19|b^2=d,d^2=e,b^a=be,f^a=f^18,f^c=f^754 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64515⋊C3, #10597347⋊C3, M16×D19⋊C3, … |
| maximal normal subgroup of | C2×#64515⋊C3, #10597347⋊C3, M16×D19⋊C3, … |
| maximal quotient of | ((C19⋊C3)⋊C4)⋊C8, #10597272⋊C3, (C2×D19⋊C3)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 8);