Finite Group DatabasebetaFinite Group Databasebeta| order | 13320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | D5×AGL(1,𝔽37) |
| Fitting, socle, derived, Hall | C5×C37 ⋊ C2×C4×C9 |
| Hall | C5×#66526 ⋊ C2×C4 |
| Hall | D5×#3866 ⋊ C9 |
| Hall | #66526 ⋊ C4×D5 |
| Sylow | C37 ⋊ C4×C9×D5 |
| Sylow | C5 ⋊ C2×AGL(1,𝔽37) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C37 | C2×C4×C9 |
| prime radical | D5×D37⋊C3 | C2×C3 |
| cosocle | C5×D37⋊C3 | C22×C3 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 185 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AGL(1,𝔽37) |
| maximal normal subgroup of | AGL(1,𝔽5)×AGL(1,𝔽37) |
Past the SmallGroups library coverage — no SmallGroups id.