Finite Group DatabasebetaFinite Group Databasebeta| order | 30660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5×C73 · Schur multiplier (H2) = C2 |
| direct product | C22×C5×ΓL(1,𝔽8)×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5×C73 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C22×C3×C5×C73 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C7×C73 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C22×C5×C73 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10220 |
7300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30660, 219);