Finite Group DatabasebetaFinite Group Databasebeta| order | 30660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C7⋊#13091735 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C7⋊#13091735 |
| commutator, hypocenter | C5×C7×C73 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C73 | C4 |
| prime radical | C3×C5×C7×D73 | C2 |
| cosocle | C5×C7×D73 | C2×C3 |
| LCS | G ▷ C5×C7×C73 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7665 |
2004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30660, 167);