Finite Group DatabasebetaFinite Group Databasebeta| order | 18278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D481 |
| unambiguous semidirect product | C13⋊(C19×D37) |
| unambiguous semidirect product | C37⋊(C19×D13) |
| Fitting, socle, Hall | C13×C19×C37 ⋊ C2 |
| derived, Hall | C13×C37 ⋊ C2×C19 |
| Hall | C19×C37 ⋊ D13 |
| Hall | C13×C19 ⋊ D37 |
| Sylow | C37 ⋊ C19×D13 |
| Sylow | C13 ⋊ C19×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D481 |
| commutator, cosocle, hypocenter | C13×C37 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C37 | C2 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9139 |
4598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#14515321, C19×#14515320, C19⋊#14515321, … |
| maximal normal subgroup of | C19×#14515321, C19×#14515320, C19⋊#14515321, … |
| maximal quotient of | C19×Dic481, C2×C19×D481 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18278, 6);