Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D5×C29×D15 |
| unambiguous semidirect product | (C3×D5)⋊(D5×C29) |
| unambiguous semidirect product | (C5×D5)⋊(D3×C29) |
| Fitting, socle, Hall | C3×C52×C29 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C29 |
| Hall | C52×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ D52 |
| Sylow | C52 ⋊ C2×D3×C29 |
| Sylow | C3 ⋊ D52×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D5×D15 |
| commutator, hypocenter | C3×C52 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C29 | |
96 conjugacy classes of subgroups.
1044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C29×D45, C29×#3874⋊D3, C3×D5×C29×D15, … |
| maximal normal subgroup of | C3×D5×C29×D15 |
| maximal quotient of | D5×C29×D45, C3×D5×C29×D15, C29×D152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 128);