Finite Group DatabasebetaFinite Group Databasebeta| order | 5796 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C23×D21 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D7×C23) |
| Fitting, socle | C2×C32×C7×C23 ⋊ C2 |
| derived | C3×C7 ⋊ C22×C3×C23 |
| Hall | C32×C7×C23 ⋊ C22 |
| Hall | C32×C23 ⋊ C2×D7 |
| Hall | C7×C23 ⋊ C2×C3×D3 |
| Hall | C32×C7 ⋊ C22×C23 |
| Sylow | C32 ⋊ C2×D7×C23 |
| Sylow | C7 ⋊ C2×C3×D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C23 | D21 |
| commutator, hypocenter | C3×C7 | C22×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C23 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C3×C23 | |
88 conjugacy classes of subgroups.
1656 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×C23×D21, C2×C3×C5×C23×D21, C2×C3×C23×D105 |
| maximal normal subgroup of | C2×C3×C5×C23×D21 |
| maximal quotient of | C3×D5×C23×D21, C2×C3×C5×C23×D21, C2×C3×C23×D105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5796, 106);