Finite Group DatabasebetaFinite Group Databasebeta| order | 30740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C5×C29×#6157 |
| Fitting, socle, Hall | C5×C29×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C5×C29 |
| Hall | C29×C53 ⋊ C4×C5 |
| Hall | C5×C53 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | #6157 |
| commutator, hypocenter | C53 | C4×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C53 | C4 |
| prime radical | C5×C29×D53 | C2 |
| cosocle | D53 | C2×C5×C29 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C5×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7685 |
2465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30740, 10);