Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic1201 |
| Sylow | C1201 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9608 |
Polycyclic presentation:
2^4,1201|a^2=d,b^a=bc,e^a=e^12004810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50307768, #50307769, C22⋊C4×D1201, … |
| maximal normal subgroup of | #50307768, #50307769, C22⋊C4×D1201, … |
| maximal quotient of | #50307761, C22⋊#23751190, #50307769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 18);