Finite Group DatabasebetaFinite Group Databasebeta| order | 8468 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#64408 |
| Fitting, socle, Hall | C29×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #64408 |
| commutator, hypocenter | C73 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C73 | C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C29 | |
12 conjugacy classes of subgroups.
638 conjugacy classes — view the full character table.
| maximal subgroup of | C29×#64408⋊C3, C3×C29×#64408, C29×C3⋊#64408 |
| maximal normal subgroup of | C29×#64408⋊C3, C3×C29×#64408 |
| maximal quotient of | C3×C29×#64408, C29×C3⋊#64408 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8468, 6);