Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#20259440 |
| Fitting | C2×C8×C383 ⋊ C2 |
| Sylow | C383 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
3076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588132, C4×#20259440, #37588303, … |
| maximal normal subgroup of | #37588132, C4×#20259440, #37588303, … |
| maximal quotient of | C2×#27133751, C4×#20259440, C2×(C2×D383)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 150);