Finite Group DatabasebetaFinite Group Databasebeta| order | 14378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×D79⋊C13 |
| unambiguous semidirect product | D79⋊(C7×C13) |
| unambiguous semidirect product | (C79⋊C13)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D79)⋊C13 |
| Fitting, socle, Hall | C7×C79 ⋊ C2×C13 |
| derived, Sylow | C79 ⋊ C2×C7×C13 |
| Hall | C7×C79⋊C13 ⋊ C2 |
| Hall | C7×D79 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C2×C7 |
| Hall | D79 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D79⋊C13 |
| commutator, cosocle, hypocenter | C79 | C2×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C79 | C2×C13 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 553 |
203 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D79⋊C13, C2×C7×D79⋊C13 |
| maximal normal subgroup of | D7×D79⋊C13, C2×C7×D79⋊C13 |
| maximal quotient of | C7×Dic79⋊C13, C2×C7×D79⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14378, 10);