Finite Group DatabasebetaFinite Group Databasebeta| order | 38025 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C25 · Schur multiplier (H2) = C3 |
| Fitting, Hall | C132×C25 ⋊ C32 |
| derived, Sylow | C132 ⋊ C32×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C13⋊C32 |
| commutator, hypocenter | C132 | C32×C25 |
| Frattini | C5 | C5×C13⋊C32 |
| Fitting | C132×C25 | C32 |
| socle, cosocle | C5×C132 | C32×C5 |
| prime radical | C5×C13⋊C32 | C5 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C25 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 975 |
1225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38025, 19);