Finite Group DatabasebetaFinite Group Databasebeta| order | 30876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×(C31⋊C3)⋊C4 |
| unambiguous semidirect product | (C31⋊C3)⋊(C4×C83) |
| unambiguous semidirect product | Dic31⋊(C3×C83) |
| unambiguous semidirect product | (C83×Dic31)⋊C3 |
| derived, Sylow | C31 ⋊ C3×C4×C83 |
| Hall | C83×Dic31 ⋊ C3 |
| Hall | C83×C31⋊C3 ⋊ C4 |
| Hall | C31×C83 ⋊ C3×C4 |
| Hall | Dic31 ⋊ C3×C83 |
| Hall | C31⋊C3 ⋊ C4×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | D31⋊C3 |
| commutator, hypocenter | C31 | C3×C4×C83 |
| Frattini | C2 | C83×D31⋊C3 |
| Fitting, socle | C2×C31×C83 | C2×C3 |
| prime radical | C2×C83×C31⋊C3 | C2 |
| cosocle | C2×C31 | C2×C3×C83 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C83 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10292 |
1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30876, 11);