Finite Group DatabasebetaFinite Group Databasebeta| order | 28975 |
| automorphism | ? |
| homology | Abelianization (H1) = C19×C25 · Schur multiplier (H2) = C1 |
| direct product | C19×C61⋊C25 |
| unambiguous semidirect product | C61⋊(C19×C25) |
| unambiguous semidirect product | (C19×C61)⋊C25 |
| derived, Sylow | C61 ⋊ C19×C25 |
| Hall | C19×C61 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | C61⋊C5 |
| commutator, hypocenter | C61 | C19×C25 |
| Frattini | C5 | C19×C61⋊C5 |
| Fitting, socle, prime radical | C5×C19×C61 | C5 |
| cosocle | C5×C61 | C5×C19 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5×C19 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28975 |
1615 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28975, 2);