Finite Group DatabasebetaFinite Group Databasebeta| order | 30291 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C439⋊C3 |
| unambiguous semidirect product | C439⋊(C3×C23) |
| unambiguous semidirect product | (C23×C439)⋊C3 |
| Fitting, socle, Hall | C23×C439 ⋊ C3 |
| derived, Sylow | C439 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C439⋊C3 |
| commutator, cosocle, hypocenter | C439 | C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C439 | C3 |
| LCS | G ▷ C439 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10097 |
3427 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30291, 1);