Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#10596816 |
| unambiguous semidirect product | C3⋊(C5×#10596816) |
| Fitting, socle, Hall | C3×C52×C29 ⋊ C4 |
| derived | C3×C5×C29 ⋊ C4×C5 |
| Hall | C52×C29 ⋊ Dic3 |
| Hall | C3×C29 ⋊ C5×AGL(1,𝔽5) |
| Hall | C3×C52 ⋊ Dic29 |
| Sylow | C29 ⋊ C5×ΓL(1,𝔽16) |
| Sylow | C52 ⋊ Dic87 |
| Sylow | C3 ⋊ C5×#10596816 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#10596816 |
| commutator, hypocenter | C3×C5×C29 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C4 |
| LCS | G ▷ C3×C5×C29 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
885 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9⋊#10596816, C3×C5×C3⋊#10596816, C5×C3⋊(C3⋊#10596816) |
| maximal normal subgroup of | C3×C5×C3⋊#10596816 |
| maximal quotient of | C5×C9⋊#10596816, C3×C5×C3⋊#10596816, C5×C3⋊(C3⋊#10596816) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 104);