Finite Group DatabasebetaFinite Group Databasebeta| order | 14413 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C7×C71) |
| Fitting, socle, Hall | C29×C71 ⋊ C7 |
| derived, Sylow | C29 ⋊ C7×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C7×C71 |
| Frattini | C1 | G |
| Fitting, socle | C29×C71 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C71 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2059 |
781 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C71×C29⋊C7, D71×C29⋊C7, C71×D29⋊C7, … |
| maximal normal subgroup of | C2×C71×C29⋊C7, D71×C29⋊C7, C71×D29⋊C7, … |
| maximal quotient of | C2×C71×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14413, 1);