Finite Group DatabasebetaFinite Group Databasebeta| order | 30772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#10597845 |
| Fitting, Hall | C49×C157 ⋊ C4 |
| derived, Sylow | C157 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #10597845 |
| commutator, hypocenter | C157 | C4×C49 |
| Frattini | C7 | C7×#10597845 |
| Fitting | C49×C157 | C4 |
| socle | C7×C157 | C4×C7 |
| prime radical, cosocle | C7×D157 | C2×C7 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7693 |
2107 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30772, 6);