Finite Group DatabasebetaFinite Group Databasebeta| order | 7812 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic217 |
| derived, Hall | C7×C31 ⋊ C32×C4 |
| Hall | C32×C7×C31 ⋊ C4 |
| Hall | C32×C31 ⋊ Dic7 |
| Hall | C32×C7 ⋊ Dic31 |
| Sylow | C31 ⋊ C32×Dic7 |
| Sylow | C7 ⋊ C32×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D217 |
| commutator, hypocenter | C7×C31 | C32×C4 |
| Frattini | C2 | C32×D217 |
| Fitting, socle | C2×C32×C7×C31 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
1980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7812, 104);