Finite Group DatabasebetaFinite Group Databasebeta| order | 5796 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C23 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C7×C3⋊D3×C23 |
| unambiguous semidirect product | (C2×C3)⋊(D3×C7×C23) |
| Fitting, socle | C2×C32×C7×C23 ⋊ C2 |
| derived, Sylow | C32 ⋊ C22×C7×C23 |
| Hall | C32×C7×C23 ⋊ C22 |
| Hall | C32×C23 ⋊ C22×C7 |
| Hall | C32×C7 ⋊ C22×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C23 | C3⋊D3 |
| commutator, hypocenter | C32 | C22×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C23 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C7×C23 | |
120 conjugacy classes of subgroups.
1932 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×C3⋊D3×C23, C2×C5×C7×C3⋊D3×C23, C2×C7×C23×C3⋊D15 |
| maximal normal subgroup of | C2×C5×C7×C3⋊D3×C23 |
| maximal quotient of | C7×D5×C3⋊D3×C23, C2×C5×C7×C3⋊D3×C23, C2×C7×C23×C3⋊D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5796, 104);