Finite Group DatabasebetaFinite Group Databasebeta| order | 30681 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#23779394 |
| Fitting, socle | C3×C7×C487 ⋊ C3 |
| derived, Hall | C7×C487 ⋊ C32 |
| Sylow | C487 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C487⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #23779394 |
| commutator, cosocle, hypocenter | C7×C487 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C487 | C3 |
| LCS | G ▷ C7×C487 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10227 |
3417 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30681, 14);