Finite Group DatabasebetaFinite Group Databasebeta| order | 2562 |
| isoclinism | isoclinic class of #13046197 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#13046197 |
| Fitting, socle, Hall | C2×C7×C61 ⋊ C3 |
| derived, Hall | C7×C61 ⋊ C2×C3 |
| Hall | C2×C61 ⋊ ΓL(1,𝔽8) |
| Sylow | C61 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C61⋊C3 |
| Sylow | C7 ⋊ C2×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13046197 |
| commutator, cosocle, hypocenter | C7×C61 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C61 | C3 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 854 |
290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2562, 4);