Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic155 |
| unambiguous semidirect product | C31⋊(Dic5×C49) |
| derived, Hall | C5×C31 ⋊ C4×C49 |
| Hall | C5×C31×C49 ⋊ C4 |
| Hall | C31×C49 ⋊ Dic5 |
| Hall | C5×C49 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic5×C49 |
| Sylow | C5 ⋊ C49×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D155 |
| commutator, hypocenter | C5×C31 | C4×C49 |
| Frattini | C2×C7 | C7×D155 |
| Fitting | C2×C5×C31×C49 | C2 |
| socle, prime radical, cosocle | C2×C5×C7×C31 | C2×C7 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C2×C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30380 |
7742 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 7);