Finite Group DatabasebetaFinite Group Databasebeta| order | 4620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×C7×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D3×D11 |
| commutator, cosocle, hypocenter | C3×C11 | C22×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C11 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C5×C7 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1155 |
735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4620, 89);