Finite Group DatabasebetaFinite Group Databasebeta| order | 30258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C41 |
| unambiguous semidirect product | C3⋊(C3⋊(C41⋊D41)) |
| unambiguous semidirect product | C41⋊(C3⋊D123) |
| Fitting, socle, derived, Hall | C32×C412 ⋊ C2 |
| Sylow | C412 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ C41⋊D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C412 | C2 |
| LCS | G ▷ C32×C412 | |
| UCS | C1 | |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15129 |
Polycyclic presentation:
2,3^2,41^2|b^a=b^2,c^a=c^2,d^a=d^40,e^a=e^407566 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30258, 34);