Finite Group DatabasebetaFinite Group Databasebeta| order | 14271 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C67⋊C3 |
| unambiguous semidirect product | C67⋊(C3×C71) |
| unambiguous semidirect product | (C67×C71)⋊C3 |
| Fitting, socle, Hall | C67×C71 ⋊ C3 |
| derived, Sylow | C67 ⋊ C3×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C67×C71 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C71 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4757 |
1775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C71×C67⋊C3, D71×C67⋊C3, C71×D67⋊C3, … |
| maximal normal subgroup of | C2×C71×C67⋊C3, D71×C67⋊C3, C71×D67⋊C3, … |
| maximal quotient of | C2×C71×C67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14271, 1);