Finite Group DatabasebetaFinite Group Databasebeta| order | 19375 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C31 · Schur multiplier (H2) = C1 |
| direct product | C5×C53⋊C31 |
| unambiguous semidirect product | C54⋊C31 |
| Fitting, socle, Sylow | C54 ⋊ C31 |
| derived | C53 ⋊ C5×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C53⋊C31 |
| commutator, cosocle, hypocenter | C53 | C5×C31 |
| Frattini | C1 | G |
| Fitting, socle | C54 | C31 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C5 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 155 |
175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19375, 60);