Finite Group DatabasebetaFinite Group Databasebeta| order | 10356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic863 |
| unambiguous semidirect product | C863⋊(C3×C4) |
| derived, Sylow | C863 ⋊ C3×C4 |
| Hall | C3×C863 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D863 |
| commutator, hypocenter | C863 | C3×C4 |
| Frattini | C2 | C3×D863 |
| Fitting, socle, prime radical | C2×C3×C863 | C2 |
| cosocle | C2×C863 | C2×C3 |
| LCS | G ▷ C863 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
2598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic863, C3×Dic2589, C32×Dic863 |
| maximal normal subgroup of | C9×Dic863, C32×Dic863 |
| maximal quotient of | C9×Dic863, C3×Dic2589, C32×Dic863 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10356, 3);