Finite Group DatabasebetaFinite Group Databasebeta| order | 7812 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C4×#10620253 |
| Fitting | C3×C4×C7×C31 ⋊ C3 |
| derived, Hall | C7×C31 ⋊ C32×C4 |
| Hall | C4×C7×C31 ⋊ C32 |
| Hall | C4×C31 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C31 ⋊ C3×C4×ΓL(1,𝔽8) |
| Hall | C4×C7 ⋊ C3×C31⋊C3 |
| Sylow | C7 ⋊ C3×C4×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #10620253 |
| commutator, hypocenter | C7×C31 | C32×C4 |
| Frattini | C2 | C2×C3×#10620253 |
| Fitting | C3×C4×C7×C31 | C3 |
| socle | C2×C3×C7×C31 | C2×C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C3×C4 | |
72 conjugacy classes of subgroups.
900 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7812, 101);