Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#16812367 |
| unambiguous semidirect product | #13181884⋊C8 |
| Fitting | C4×C433 ⋊ C8 |
| derived, Sylow | C433 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16812367 |
| commutator, hypocenter | C433 | C4×C8 |
| Frattini | C2 | C2×#16812367 |
| Fitting | C4×C433 | C8 |
| socle | C2×C433 | C2×C8 |
| prime radical | C2×D433 | C2×C4 |
| cosocle | C2×#13181884 | C22 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1732 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#16812367, #42122895, D4⋊#16812367, … |
| maximal normal subgroup of | C8×#16812367, #42122895, D4⋊#16812367, … |
| maximal quotient of | C8×#16812367, #42122895, (C2×#16812367)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 237);