Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of (C19⋊C3)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×(C19⋊C3)⋊Q8 |
| unambiguous semidirect product | (C2×C19⋊C3)⋊Q8 |
| unambiguous semidirect product | (C2×Dic38)⋊C3 |
| Hall | C2×Dic38 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×Q8 |
| Sylow | C19 ⋊ C2×C3×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #10597267⋊C3, #10597273⋊C3, #10597281⋊C3, … |
| maximal normal subgroup of | #10597267⋊C3, #10597273⋊C3, #10597281⋊C3, … |
| maximal quotient of | C4×(C19⋊C3)⋊Q8, #10597315⋊C3, #10597316⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 120);