Finite Group DatabasebetaFinite Group Databasebeta| order | 8134 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C83 · Schur multiplier (H2) = C1 |
| direct product | C7×D7×C83 |
| unambiguous semidirect product | C7⋊(C2×C7×C83) |
| Fitting, socle, Hall | C72×C83 ⋊ C2 |
| derived | C7 ⋊ C2×C7×C83 |
| Sylow | C72 ⋊ C2×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C83 | D7 |
| commutator, hypocenter | C7 | C2×C7×C83 |
| Frattini | C1 | G |
| Fitting, socle | C72×C83 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C7×C83 | |
22 conjugacy classes of subgroups.
2905 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D83, D72×C83, D7×D581, … |
| maximal normal subgroup of | C7×D7×D83, D72×C83, D7×D581, … |
| maximal quotient of | C7×Dic7×C83, C2×C7×D7×C83, C3×C7×D7×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8134, 7);