Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#18012450 |
| unambiguous semidirect product | (C2×#18012450)⋊C2 |
| Fitting | C22×C1201 ⋊ C4 |
| Sylow | C1201 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4804 |
Polycyclic presentation:
2^4,1201|a^2=d,b^a=bc,e^a=e^1152,e^d=e^12001210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50307912, #50307913, C2×C22⋊#18012450, … |
| maximal normal subgroup of | #50307912, #50307913, C2×C22⋊#18012450, … |
| maximal quotient of | (C2×#18012450)⋊C4, C22⋊#23751197, #50307911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 45);