Finite Group DatabasebetaFinite Group Databasebeta| order | 8468 |
| automorphism | Aut(G) order 8535744 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4234 |
| direct product | C2×D2117 |
| unambiguous semidirect product | (C2×C29)⋊D73 |
| unambiguous semidirect product | (C2×C73)⋊D29 |
| Fitting, socle | C2×C29×C73 ⋊ C2 |
| derived, Hall | C29×C73 ⋊ C22 |
| Sylow | C73 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2117 |
| commutator, hypocenter | C29×C73 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C73 | C2 |
| LCS | G ▷ C29×C73 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29⋊(D73⋊C3), D3×D2117, C2×C3×D2117, … |
| maximal normal subgroup of | C2×C29⋊(D73⋊C3), C2×C3×D2117, D8468 |
| maximal quotient of | D3×D2117, C2×C3×D2117, C2×D6351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8468, 13);