Finite Group DatabasebetaFinite Group Databasebeta| order | 30660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C73 · Schur multiplier (H2) = C1 |
| direct product | C7×ΓL(1,𝔽16)×C73 |
| unambiguous semidirect product | C3⋊(C7×AGL(1,𝔽5)×C73) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C73 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C4×C7×C73 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C73 | C4 |
| prime radical | C3×C7×D5×C73 | C2 |
| cosocle | C3×D5 | C2×C7×C73 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C7×C73 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7665 |
4599 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30660, 181);