Finite Group DatabasebetaFinite Group Databasebeta| order | 3255 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#10620252 |
| Fitting, socle, Hall | C5×C7×C31 ⋊ C3 |
| derived, Hall | C7×C31 ⋊ C3×C5 |
| Hall | C5×C31 ⋊ ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C5×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C5×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #10620252 |
| commutator, cosocle, hypocenter | C7×C31 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C31 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1085 |
375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3255, 6);