Finite Group DatabasebetaFinite Group Databasebeta| order | 14413 |
| isoclinism | isoclinic class of C71⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C71⋊C7 |
| unambiguous semidirect product | C71⋊(C7×C29) |
| Fitting, socle, Hall | C29×C71 ⋊ C7 |
| derived, Sylow | C71 ⋊ C7×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C71 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C29 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2059 |
493 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29×C71⋊C7, C29×D71⋊C7, D29×C71⋊C7, … |
| maximal normal subgroup of | C2×C29×C71⋊C7, C29×D71⋊C7, D29×C71⋊C7, … |
| maximal quotient of | C2×C29×C71⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14413, 2);