Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D1532 |
| Fitting | C42×C383 ⋊ C2 |
| Sylow | C383 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
3076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588078, #37588080, #37588416, … |
| maximal normal subgroup of | #37588078, #37588080, #37588416, … |
| maximal quotient of | C4×(C2×D383)⋊C4, C4×C4⋊Dic383, #37588225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 110);