Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×D192 |
| unambiguous semidirect product | (C19×D19)⋊(C2×C25) |
| Fitting, Hall | C192×C25 ⋊ C22 |
| derived, Sylow | C192 ⋊ C22×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D192 |
| commutator, hypocenter | C192 | C22×C25 |
| Frattini | C5 | C5×D192 |
| Fitting | C192×C25 | C22 |
| socle, cosocle | C5×C192 | C22×C5 |
| prime radical | C5×D192 | C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C25 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 950 |
3025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 53);