Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C3⋊(#6923⋊C5) |
| unambiguous semidirect product | C3⋊(C5×#6923⋊C5) |
| unambiguous semidirect product | (C3⋊#6923)⋊C52 |
| unambiguous semidirect product | (C5×C3⋊#6923)⋊C5 |
| Fitting, socle | C3×C5×C61 ⋊ C4×C5 |
| derived, Hall | C3×C61 ⋊ C4×C52 |
| Hall | C3×C5×C61⋊C5 ⋊ C4 |
| Hall | C5×C61⋊C5 ⋊ Dic3 |
| Hall | C3⋊#6923 ⋊ C52 |
| Sylow | C61 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C5×#6923⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(#6923⋊C5) |
| commutator, hypocenter | C3×C61 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C61 | C4×C5 |
| prime radical | C3×C5×D61⋊C5 | C2 |
| cosocle | C3×D61 | C2×C52 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 915 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 129);