Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#20294105 |
| derived, Sylow | C433 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #13181884 |
| commutator, hypocenter | C433 | C22×C8 |
| Frattini | C2 | C22×#13181884 |
| Fitting | C2×C4×C433 | C4 |
| socle | C22×C433 | C2×C4 |
| prime radical | C22×D433 | C4 |
| cosocle | Dic433 | C23 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42122676, #42122684, #42122686, … |
| maximal normal subgroup of | #42122676, #42122684, #42122686, … |
| maximal quotient of | C2×C4×#16812365, C4×#20294105, #42122779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 229);