Finite Group DatabasebetaFinite Group Databasebeta| order | 8468 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×Dic29 |
| derived, Sylow | C29 ⋊ C4×C73 |
| Hall | C29×C73 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C73 | D29 |
| commutator, hypocenter | C29 | C4×C73 |
| Frattini | C2 | D29×C73 |
| Fitting, socle | C2×C29×C73 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C73 | |
12 conjugacy classes of subgroups.
2336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C73×Dic29, C73×Dic87, Dic29×C73⋊C3 |
| maximal normal subgroup of | C3×C73×Dic29, Dic29×C73⋊C3 |
| maximal quotient of | C3×C73×Dic29, C73×Dic87 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8468, 2);