Finite Group DatabasebetaFinite Group Databasebeta| order | 30876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊((C31⋊C3)⋊C4) |
| unambiguous semidirect product | (C31⋊C3)⋊Dic83 |
| unambiguous semidirect product | Dic2573⋊C3 |
| derived, Hall | C31×C83 ⋊ C3×C4 |
| Hall | Dic2573 ⋊ C3 |
| Hall | C83×C31⋊C3 ⋊ C4 |
| Hall | C31⋊C3 ⋊ Dic83 |
| Sylow | C83 ⋊ (C31⋊C3)⋊C4 |
| Sylow | C31 ⋊ C3×Dic83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C83⋊(D31⋊C3) |
| commutator, hypocenter | C31×C83 | C3×C4 |
| Fitting, socle, cosocle | C2×C31×C83 | C2×C3 |
| prime radical | C2×C83×C31⋊C3 | C2 |
| LCS | G ▷ C31×C83 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10292 |
Polycyclic presentation:
2,3,31,83,2|a^2=e,c^a=c^30,d^a=d^82,c^b=c^251088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30876, 12);