Finite Group DatabasebetaFinite Group Databasebeta| order | 30605 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C6121⋊C5 |
| Fitting, socle, derived, Sylow | C6121 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6121 | C5 |
| LCS | G ▷ C6121 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6121 |
Polycyclic presentation:
5,6121|b^a=b^22341229 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30605, 1);