Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11 |
| direct product | C3×#27130894 |
| Fitting, socle | C3×C5×C112 ⋊ C4×C5 |
| derived | C5×C112 ⋊ C3×C4×C5 |
| Hall | C3×C5×#10597245 ⋊ C4 |
| Hall | C5×#10597245 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C112 ⋊ C3×C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #27130894 |
| commutator, hypocenter | C5×C112 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C4×C5 |
| prime radical | C3×D5×#10597245 | C2 |
| cosocle | D5×C112 | C2×C3×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 524);