Finite Group DatabasebetaFinite Group Databasebeta| order | 14858 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D437 |
| unambiguous semidirect product | C19⋊(C17×D23) |
| unambiguous semidirect product | C23⋊(C17×D19) |
| Fitting, socle, Hall | C17×C19×C23 ⋊ C2 |
| derived, Hall | C19×C23 ⋊ C2×C17 |
| Hall | C17×C23 ⋊ D19 |
| Hall | C17×C19 ⋊ D23 |
| Sylow | C23 ⋊ C17×D19 |
| Sylow | C19 ⋊ C17×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D437 |
| commutator, cosocle, hypocenter | C19×C23 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C19×C23 | C2 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7429 |
3740 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D19×D23, D17×D437, D323⋊D23, … |
| maximal normal subgroup of | C17×D19×D23, D17×D437, D323⋊D23, … |
| maximal quotient of | C17×Dic437, C2×C17×D437 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14858, 4);