Finite Group DatabasebetaFinite Group Databasebeta| order | 24990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D255 |
| unambiguous semidirect product | C3⋊(C49×D85) |
| unambiguous semidirect product | C5⋊(C49×D51) |
| unambiguous semidirect product | C17⋊(D15×C49) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D255 |
| commutator, hypocenter | C3×C5×C17 | C2×C49 |
| Frattini | C7 | C7×D255 |
| Fitting | C3×C5×C17×C49 | C2 |
| socle, cosocle | C3×C5×C7×C17 | C2×C7 |
| prime radical | C7×D255 | C7 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C49 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12495 |
6321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24990, 15);