Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic766 |
| Sylow | C383 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
3076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588081, #37588083, C4×#20259445, … |
| maximal normal subgroup of | #37588081, #37588083, C4×#20259445, … |
| maximal quotient of | C4×C4⋊Dic383, C4×Dic383⋊C4, #37588234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 112);