Finite Group DatabasebetaFinite Group Databasebeta| order | 36518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C312 · Schur multiplier (H2) = C31 |
| direct product | C312×D19 |
| unambiguous semidirect product | C19⋊(C2×C312) |
| Fitting, socle, Hall | C19×C312 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C312 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C312 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C312 |
| Frattini | C1 | G |
| Fitting, socle | C19×C312 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C312 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18259 |
10571 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36518, 8);