Finite Group DatabasebetaFinite Group Databasebeta| order | 14378 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C79 · Schur multiplier (H2) = C1 |
| direct product | C13×D7×C79 |
| unambiguous semidirect product | C7⋊(C2×C13×C79) |
| Fitting, socle, Hall | C7×C13×C79 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C13×C79 |
| Hall | C7×C79 ⋊ C2×C13 |
| Hall | C7×C13 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C79 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C13×C79 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C79 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C13×C79 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7189 |
5135 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D7×D79, D7×D13×C79, D7×D1027, … |
| maximal normal subgroup of | C13×D7×D79, D7×D13×C79, D7×D1027, … |
| maximal quotient of | C13×Dic7×C79, C2×C13×D7×C79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14378, 6);