Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic1193 |
| Sylow | C1193 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9544 |
Polycyclic presentation:
2^4,1193|a^2=d,b^a=bc,e^a=e^11924778 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50302886, #50302887, C22⋊C4×D1193, … |
| maximal normal subgroup of | #50302886, #50302887, C22⋊C4×D1193, … |
| maximal quotient of | #50302879, C22⋊#23750841, #50302887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 18);