Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#6923⋊C25 |
| unambiguous semidirect product | (C3×#6923)⋊C25 |
| derived, Sylow | C61 ⋊ C3×C4×C25 |
| Hall | C3×C61⋊C25 ⋊ C4 |
| Hall | C61⋊C25 ⋊ C3×C4 |
| Hall | C3×#6923 ⋊ C25 |
| Hall | #6923 ⋊ C3×C25 |
| Hall | C3×C61 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #6923⋊C5 |
| commutator, hypocenter | C61 | C3×C4×C25 |
| Frattini | C5 | C3×#6923⋊C5 |
| Fitting, socle | C3×C5×C61 | C4×C5 |
| prime radical | C3×C5×D61 | C2×C5 |
| cosocle | C5×D61 | C2×C3×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4575 |
345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 22);