Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#13133324) |
| Fitting, derived, Hall | C32×C17×C25 ⋊ C4 |
| Hall | C17×C25 ⋊ C3⋊Dic3 |
| Hall | C32×C25 ⋊ #595 |
| Hall | C32×C17 ⋊ #1035 |
| Sylow | C25 ⋊ C3⋊(C3⋊#595) |
| Sylow | C17 ⋊ C3⋊(C3⋊#1035) |
| Sylow | C32 ⋊ #13133324 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C17×C25 | C4 |
| Frattini | C5 | C3⋊(C3⋊#66776) |
| socle | C32×C5×C17 | AGL(1,𝔽5) |
| prime radical, cosocle | C32×D425 | C2 |
| LCS | G ▷ C32×C17×C25 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3825 |
Polycyclic presentation:
2^2,3^2,5,17,5|a^2=b,e^5=g,c^a=c^2,d^a=d^2,e^a=e^2g,f^a=f^4,g^a=g^2,e^b=e^4g^4,f^b=f^16,g^b=g^4966 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 91);