Finite Group DatabasebetaFinite Group Databasebeta| order | 19375 |
| automorphism | ? |
| homology | Abelianization (H1) = C54 · Schur multiplier (H2) = C56 |
| direct product | C53×ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊C54 |
| unambiguous semidirect product | (C5×C31)⋊C53 |
| Fitting, socle | C53×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C54 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C54 |
| Frattini | C1 | G |
| Fitting, socle | C53×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C53 | |
2240 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, 59);