Finite Group DatabasebetaFinite Group Databasebeta| order | 36075 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C13 · Schur multiplier (H2) = C5 |
| direct product | C52×C13×C37⋊C3 |
| unambiguous semidirect product | C37⋊(C3×C52×C13) |
| unambiguous semidirect product | (C5×C37)⋊(C3×C5×C13) |
| Fitting, socle, Hall | C52×C13×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C52×C13 |
| Hall | C52×C37 ⋊ C3×C13 |
| Hall | C13×C37 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C13 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C3×C52×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C52×C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12025 |
4875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36075, 12);