Finite Group DatabasebetaFinite Group Databasebeta| order | 25830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C41×D21 |
| unambiguous semidirect product | C3⋊(C3×C5×D7×C41) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C41 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C3×C5×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C41 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C3×C5×C41 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8610 |
7380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25830, 83);