Finite Group DatabasebetaFinite Group Databasebeta| order | 8642 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C149 · Schur multiplier (H2) = C1 |
| direct product | D29×C149 |
| unambiguous semidirect product | C29⋊(C2×C149) |
| Fitting, socle, Hall | C29×C149 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C149 | D29 |
| commutator, hypocenter | C29 | C2×C149 |
| Frattini | C1 | G |
| Fitting, socle | C29×C149 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C149 | |
8 conjugacy classes of subgroups.
2384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1181×C149, #31772229, D29×D149, … |
| maximal normal subgroup of | #1181×C149, #31772229, D29×D149, … |
| maximal quotient of | Dic29×C149, C2×D29×C149, C3×D29×C149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8642, 1);