Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1201 ⋊ Q16 |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19216 |
Polycyclic presentation:
2^4,1201|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^12003007 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D1201, C2×#34063513, #50307874, … |
| maximal normal subgroup of | Q16×D1201, C2×#34063513, #50307874, … |
| maximal quotient of | #50307777, #50307778, #50307787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 30);