Finite Group DatabasebetaFinite Group Databasebeta| order | 14898 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C191 · Schur multiplier (H2) = C1 |
| direct product | D39×C191 |
| unambiguous semidirect product | C3⋊(D13×C191) |
| unambiguous semidirect product | C13⋊(D3×C191) |
| Fitting, socle, Hall | C3×C13×C191 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C191 |
| Hall | C13×C191 ⋊ D3 |
| Hall | C3×C191 ⋊ D13 |
| Sylow | C13 ⋊ D3×C191 |
| Sylow | C3 ⋊ D13×C191 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C191 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C2×C191 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C191 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C191 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7449 |
4011 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D39×D191, D3×D13×C191, D39⋊D191, … |
| maximal normal subgroup of | D39×D191, D3×D13×C191, D39⋊D191, … |
| maximal quotient of | Dic39×C191, C2×D39×C191 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14898, 8);