Finite Group DatabasebetaFinite Group Databasebeta| order | 30222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#10620321⋊C2 |
| unambiguous semidirect product | #10620321⋊(C2×C23) |
| derived, Sylow | C73 ⋊ C2×C9×C23 |
| Hall | C23×#10620321 ⋊ C2 |
| Hall | C23×D73 ⋊ C9 |
| Hall | C23×C73 ⋊ C2×C9 |
| Hall | #10620321 ⋊ C2×C23 |
| Hall | D73 ⋊ C9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | D73⋊C3 |
| commutator, hypocenter | C73 | C2×C9×C23 |
| Frattini | C3 | C23×D73⋊C3 |
| Fitting, socle | C3×C23×C73 | C2×C3 |
| prime radical | C3×C23×D73 | C3 |
| cosocle | C3×C73 | C2×C3×C23 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15111 |
1242 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30222, 10);