Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#13181884 |
| unambiguous semidirect product | D433⋊C42 |
| Fitting | C2×C4×C433 ⋊ C4 |
| derived, Sylow | C433 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3464 |
896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42122676, #42122681, #42122683, … |
| maximal normal subgroup of | #42122676, #42122681, #42122683, … |
| maximal quotient of | C42×#13181884, C2×(C2×#13181884)⋊C4, #42122747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 222);