Finite Group DatabasebetaFinite Group Databasebeta| order | 14758 |
| isoclinism | isoclinic class of D157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D157 |
| unambiguous semidirect product | C157⋊(C2×C47) |
| Fitting, socle, Hall | C47×C157 ⋊ C2 |
| derived, Sylow | C157 ⋊ C2×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D157 |
| commutator, cosocle, hypocenter | C157 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C47×C157 | C2 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C47 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7379 |
3760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#10597845, C47⋊#10597845, D47×D157, … |
| maximal normal subgroup of | C47×#10597845, C47⋊#10597845, D47×D157, … |
| maximal quotient of | C47×Dic157, C2×C47×D157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14758, 2);