Finite Group DatabasebetaFinite Group Databasebeta| order | 30660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1533 |
| unambiguous semidirect product | C3⋊(C5×Dic511) |
| unambiguous semidirect product | C7⋊(C5×Dic219) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1533 |
| commutator, hypocenter | C3×C7×C73 | C4×C5 |
| Frattini | C2 | C5×D1533 |
| Fitting, socle, prime radical | C2×C3×C5×C7×C73 | C2 |
| cosocle | C2×C3×C7×C73 | C2×C5 |
| LCS | G ▷ C3×C7×C73 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30660 |
7680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30660, 16);