Finite Group DatabasebetaFinite Group Databasebeta| order | 6700 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C67 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D5×C67 |
| unambiguous semidirect product | C5⋊(C22×C5×C67) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C5×C67) |
| Fitting, socle | C2×C52×C67 ⋊ C2 |
| derived | C5 ⋊ C22×C5×C67 |
| Hall | C52×C67 ⋊ C22 |
| Sylow | C52 ⋊ C22×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C67 | D5 |
| commutator, hypocenter | C5 | C22×C5×C67 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C67 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C5×C67 | |
48 conjugacy classes of subgroups.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C67×#3874, C2×C5×D5×C67⋊C3, C5×D3×D5×C67, … |
| maximal normal subgroup of | C2×C5×D5×C67⋊C3, C2×C3×C5×D5×C67 |
| maximal quotient of | C5×D3×D5×C67, C2×C3×C5×D5×C67, C2×C5×D15×C67 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6700, 35);