Finite Group DatabasebetaFinite Group Databasebeta| order | 30876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C31⋊C3×D83 |
| unambiguous semidirect product | C83⋊(C22×C31⋊C3) |
| unambiguous semidirect product | (C2×C83)⋊(C2×C31⋊C3) |
| unambiguous semidirect product | (C2×C31×D83)⋊C3 |
| Fitting, socle | C2×C31×C83 ⋊ C2×C3 |
| derived, Hall | C31×C83 ⋊ C22×C3 |
| Hall | C2×C31×D83 ⋊ C3 |
| Hall | C83×C31⋊C3 ⋊ C22 |
| Sylow | C83 ⋊ C22×C31⋊C3 |
| Sylow | C31 ⋊ C2×C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C31⋊C3×D83 |
| commutator, cosocle, hypocenter | C31×C83 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C83 | C2×C3 |
| LCS | G ▷ C31×C83 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5146 |
1118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30876, 17);