Finite Group DatabasebetaFinite Group Databasebeta| order | 19375 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C125 · Schur multiplier (H2) = C5 |
| direct product | C125×ΓL(1,𝔽32) |
| Fitting | C31×C125 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C125 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C125 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C5×C125 |
| Frattini | C25 | C5×ΓL(1,𝔽32) |
| Fitting | C31×C125 | C5 |
| socle | C5×C31 | C5×C25 |
| prime radical | C5×ΓL(1,𝔽32) | C25 |
| cosocle | C25×C31 | C52 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C125 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3875 |
1375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19375, 25);