Finite Group DatabasebetaFinite Group Databasebeta| order | 36417 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C199 · Schur multiplier (H2) = C1 |
| direct product | C61⋊C3×C199 |
| unambiguous semidirect product | C61⋊(C3×C199) |
| Fitting, socle, Hall | C61×C199 ⋊ C3 |
| derived, Sylow | C61 ⋊ C3×C199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C199 | C61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C3×C199 |
| Frattini | C1 | G |
| Fitting, socle | C61×C199 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C199 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12139 |
4577 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36417, 1);