Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×(C112⋊C3)⋊C5 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C112⋊C3)⋊C5 |
| unambiguous semidirect product | (AGL(1,𝔽5)×#10597243)⋊C3 |
| Fitting, socle, derived | C5×C112 ⋊ C3×C4×C5 |
| Hall | AGL(1,𝔽5)×#10597243 ⋊ C3 |
| Hall | C5×(C112⋊C3)⋊C5 ⋊ C4 |
| Hall | C5×#10597243 ⋊ C3×C4 |
| Hall | C112⋊C3 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C112 ⋊ C3×C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C112 | C3×C4×C5 |
| prime radical | D5×(C112⋊C3)⋊C5 | C2 |
| cosocle | D5×C112 | C2×C3×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 165 |
115 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 477);