Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C383 ⋊ C2 |
| Sylow | C383 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^382,d^b=de,f^b=f^3821921 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588520, #37588521, #37588525, … |
| maximal normal subgroup of | #37588520, #37588521, #37588525, … |
| maximal quotient of | #37588353, #37588357, #37588393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 174);