Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×Dic51 |
| unambiguous semidirect product | C3⋊(Dic17×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×Dic51)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D51×ΓL(1,𝔽32) |
| commutator, hypocenter | C3×C17×C31 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C17×C31 | C2×C5 |
| prime radical | C2×C3×C17×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C3×C17×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6324 |
594 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 25);