Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#13133343⋊C3 |
| unambiguous semidirect product | #13133343⋊C32 |
| unambiguous semidirect product | (C3×#13133343)⋊C3 |
| Fitting, socle | C3×C52×C17 ⋊ C3×C4 |
| derived, Hall | C52×C17 ⋊ C32×C4 |
| Hall | C3×C17×C52⋊C3 ⋊ C4 |
| Hall | #13133343 ⋊ C32 |
| Hall | C3×C52⋊C3 ⋊ #595 |
| Sylow | C52 ⋊ C32×#595 |
| Sylow | C17 ⋊ C3×#1043⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13133343⋊C3 |
| commutator, hypocenter | C52×C17 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C3×C4 |
| prime radical | C3×C17⋊((C5⋊D5)⋊C3) | C2 |
| cosocle | C5⋊D85 | C2×C32 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 263);