Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C5×#92150⋊C5 |
| unambiguous semidirect product | (C3×#92150)⋊C52 |
| unambiguous semidirect product | (C3×C5×#92150)⋊C5 |
| Fitting, socle | C3×C5×C112 ⋊ C4×C5 |
| derived, Sylow | C112 ⋊ C3×C4×C52 |
| Hall | C3×C5×#10597243 ⋊ C4 |
| Hall | C5×#10597243 ⋊ C3×C4 |
| Hall | C3×#92150 ⋊ C52 |
| Hall | #92150 ⋊ C3×C52 |
| Hall | C3×C112 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #92150⋊C5 |
| commutator, hypocenter | C112 | C3×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C4×C5 |
| prime radical | C3×C5×#11925892 | C2 |
| cosocle | C11⋊D11 | C2×C3×C52 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3×C5 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 502);