Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽32)⋊Dic5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊Dic15 |
| unambiguous semidirect product | Dic465⋊C5 |
| derived | C3×C5×C31 ⋊ C4×C5 |
| Hall | C3×C5×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C5×ΓL(1,𝔽32) ⋊ Dic3 |
| Hall | C3×C31 ⋊ C5×Dic5 |
| Sylow | C31 ⋊ C5×Dic15 |
| Sylow | C3 ⋊ ΓL(1,𝔽32)⋊Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊(D31⋊C5)) |
| commutator, hypocenter | C3×C5×C31 | C4×C5 |
| Fitting, socle | C2×C3×C5×C31 | C2×C5 |
| LCS | G ▷ C3×C5×C31 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,5,31,2|a^2=f,c^a=c^2,d^a=d^4,e^a=e^30,e^b=e^16180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 66);