Finite Group DatabasebetaFinite Group Databasebeta| order | 30681 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#17983940 |
| Fitting, socle, Hall | C7×C487 ⋊ C9 |
| derived, Sylow | C487 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #17983940 |
| commutator, hypocenter | C487 | C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C7×C487 | C9 |
| prime radical | C7×C487⋊C3 | C3 |
| cosocle | C487⋊C3 | C3×C7 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3409 |
441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30681, 7);