Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13133344⋊C9 |
| derived, Hall | C52×C17 ⋊ C4×C9 |
| Hall | C17×C52⋊C9 ⋊ C4 |
| Hall | #13133344 ⋊ C9 |
| Hall | C52⋊C9 ⋊ #595 |
| Sylow | C52 ⋊ C9×#595 |
| Sylow | C17 ⋊ #1043⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #13133344⋊C3 |
| commutator, hypocenter | C52×C17 | C4×C9 |
| Fitting, socle | C3×C52×C17 | C3×C4 |
| prime radical, cosocle | C3×C5⋊D85 | C2×C3 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
Polycyclic presentation:
2,3,2,5^2,17,3|a^2=c,b^3=g,d^a=d^3,e^a=e^3,f^a=f^13,d^b=de,e^b=d^2e^3,d^c=d^4,e^c=e^4,f^c=f^16174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 138);