Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic766 |
| Sylow | C383 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
3076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588255, #37588256, #37588257, … |
| maximal normal subgroup of | #37588255, #37588256, #37588257, … |
| maximal quotient of | C22×Dic383⋊C4, C22×C4⋊Dic383, C2×C4×Dic766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 186);