Finite Group DatabasebetaFinite Group Databasebeta| order | 19232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C601 ⋊ C2 |
| Sylow | C601 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4808 |
Polycyclic presentation:
2^5,601|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^6003014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D601, C2×#34063751, #50308691, … |
| maximal normal subgroup of | #104×D601, C2×#34063751, #50308691, … |
| maximal quotient of | #50308403, #50308406, #50308411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19232, 72);