Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9 · Schur multiplier (H2) = C36 |
| direct product | C33×#11765919 |
| unambiguous semidirect product | (C127⋊C3)⋊(C32×C9) |
| Fitting, socle | C33×C127 ⋊ C9 |
| derived, Sylow | C127 ⋊ C33×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | #11765919 |
| commutator, hypocenter | C127 | C33×C9 |
| Frattini | C1 | G |
| Fitting, socle | C33×C127 | C9 |
| prime radical | C33×C127⋊C3 | C3 |
| cosocle | C127⋊C3 | C34 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C33 | |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3429 |
621 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 361);