Finite Group DatabasebetaFinite Group Databasebeta| order | 6700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D67 |
| unambiguous semidirect product | (D5×C67)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D67)⋊(C2×C5) |
| unambiguous semidirect product | D335⋊(C2×C5) |
| Fitting, socle, Hall | C52×C67 ⋊ C22 |
| derived | C5×C67 ⋊ C22×C5 |
| Sylow | C67 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D67 |
| commutator, hypocenter | C5×C67 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C67 | C22 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D67×#3874, C5×D5×D67⋊C3, C3×C5×D5×D67, … |
| maximal normal subgroup of | C5×D5×D67⋊C3, C3×C5×D5×D67 |
| maximal quotient of | C3×C5×D5×D67, C5×D15×D67, C5×D5×D201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6700, 21);