Finite Group DatabasebetaFinite Group Databasebeta| order | 5796 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C7×D69 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C7×D23) |
| unambiguous semidirect product | (C2×C23)⋊(C3×D3×C7) |
| Fitting, socle | C2×C32×C7×C23 ⋊ C2 |
| derived | C3×C23 ⋊ C22×C3×C7 |
| Hall | C32×C7×C23 ⋊ C22 |
| Hall | C32×C23 ⋊ C22×C7 |
| Hall | C7×C23 ⋊ C2×C3×D3 |
| Hall | C32×C7 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C3×D3×C7 |
| Sylow | C32 ⋊ C2×C7×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D69 |
| commutator, hypocenter | C3×C23 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C3×C7 | |
88 conjugacy classes of subgroups.
1512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D5×D69, C2×C3×C5×C7×D69, C2×C3×C7×D345 |
| maximal normal subgroup of | C2×C3×C5×C7×D69 |
| maximal quotient of | C3×C7×D5×D69, C2×C3×C5×C7×D69, C2×C3×C7×D345 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5796, 107);