Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C3⋊#1035 |
| unambiguous semidirect product | C3⋊(C29×#1035) |
| Fitting, Hall | C3×C25×C29 ⋊ C4 |
| derived, Hall | C3×C25 ⋊ C4×C29 |
| Hall | C25×C29 ⋊ Dic3 |
| Hall | C3×C29 ⋊ #1035 |
| Sylow | C25 ⋊ Dic3×C29 |
| Sylow | C3 ⋊ C29×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C4×C29 |
| Frattini | C5 | C29×ΓL(1,𝔽16) |
| Fitting | C3×C25×C29 | C4 |
| socle | C3×C5×C29 | AGL(1,𝔽5) |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C29 | |
36 conjugacy classes of subgroups.
696 conjugacy classes — view the full character table.
| maximal subgroup of | C29×C9⋊#1035, C3×C29×C3⋊#1035, C29×C3⋊(C3⋊#1035) |
| maximal normal subgroup of | C3×C29×C3⋊#1035 |
| maximal quotient of | C29×C9⋊#1035, C3×C29×C3⋊#1035, C29×C3⋊(C3⋊#1035) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 17);