Finite Group DatabasebetaFinite Group Databasebeta| order | 30258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C41 |
| unambiguous semidirect product | (C41⋊D41)⋊C9 |
| derived, Sylow | C412 ⋊ C2×C9 |
| Hall | C412⋊C9 ⋊ C2 |
| Hall | C41⋊D41 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C41⋊D41)⋊C3 |
| commutator, hypocenter | C412 | C2×C9 |
| Fitting, socle, cosocle | C3×C412 | C2×C3 |
| prime radical | C3×C41⋊D41 | C3 |
| LCS | G ▷ C412 | |
| UCS | C1 ◁ C3 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 369 |
Polycyclic presentation:
2,3,41^2,3|b^3=e,c^a=c^40,d^a=d^40,c^b=c^28d^14,d^b=c^21d^12858 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30258, 13);