Finite Group DatabasebetaFinite Group Databasebeta| order | 30740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#11761507 |
| Fitting, socle, Hall | C5×C29×C53 ⋊ C4 |
| derived, Hall | C5×C53 ⋊ C4×C29 |
| Hall | C29×C53 ⋊ AGL(1,𝔽5) |
| Hall | C5×C29 ⋊ Dic53 |
| Sylow | C53 ⋊ AGL(1,𝔽5)×C29 |
| Sylow | C5 ⋊ C29×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #11761507 |
| commutator, hypocenter | C5×C53 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C53 | C4 |
| prime radical | D5×C29×C53 | C2 |
| cosocle | D5×C53 | C2×C29 |
| LCS | G ▷ C5×C53 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7685 |
3161 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30740, 20);