Finite Group DatabasebetaFinite Group Databasebeta| order | 12016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C751 ⋊ C2 |
| Sylow | C751 ⋊ SD16 |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,751|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^7501882 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D751, C2×#26046629, #37562458, … |
| maximal normal subgroup of | SD16×D751, C2×#26046629, #37562458, … |
| maximal quotient of | #37562358, #37562362, #37562369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12016, 27);