Finite Group DatabasebetaFinite Group Databasebeta| order | 14378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | D7×C79⋊C13 |
| unambiguous semidirect product | C7⋊(C2×C79⋊C13) |
| unambiguous semidirect product | (D7×C79)⋊C13 |
| Fitting, socle, derived, Hall | C7×C79 ⋊ C2×C13 |
| Hall | C7×C79⋊C13 ⋊ C2 |
| Hall | D7×C79 ⋊ C13 |
| Sylow | C79 ⋊ C13×D7 |
| Sylow | C7 ⋊ C2×C79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C79 | C2×C13 |
| LCS | G ▷ C7×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 553 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D79⋊C13, C2×D7×C79⋊C13 |
| maximal normal subgroup of | D7×D79⋊C13, C2×D7×C79⋊C13 |
| maximal quotient of | Dic7×C79⋊C13, C2×D7×C79⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14378, 11);