Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #13133334⋊C9 |
| derived, Hall | C52×C17 ⋊ C4×C9 |
| Hall | C17×C52⋊C9 ⋊ C4 |
| Hall | #13133334 ⋊ C9 |
| Hall | C52⋊C9 ⋊ Dic17 |
| Sylow | C52 ⋊ C9×Dic17 |
| Sylow | C17 ⋊ #1039⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C17⋊((C5⋊D5)⋊C3) |
| commutator, hypocenter | C52×C17 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C17 | C2×C3 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3060 |
Polycyclic presentation:
2,3,5^2,17,2,3|a^2=f,b^3=g,c^a=c^4,d^a=d^4,e^a=e^16,c^b=cd,d^b=c^2d^3588 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 53);