Finite Group DatabasebetaFinite Group Databasebeta| order | 5964 |
| automorphism | Aut(G) order 2504880 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2982 |
| direct product | C2×D1491 |
| unambiguous semidirect product | (C2×C3)⋊D497 |
| unambiguous semidirect product | (C2×C7)⋊D213 |
| unambiguous semidirect product | (C2×C71)⋊D21 |
| Fitting, socle | C2×C3×C7×C71 ⋊ C2 |
| derived, Hall | C3×C7×C71 ⋊ C22 |
| Hall | C7×C71 ⋊ C2×D3 |
| Hall | C3×C71 ⋊ C2×D7 |
| Sylow | C71 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D71 |
| Sylow | C7 ⋊ C2×D213 |
| Sylow | C3 ⋊ C2×D497 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1491 |
| commutator, hypocenter | C3×C7×C71 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C71 | C2 |
| LCS | G ▷ C3×C7×C71 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1494 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4473, C2×C3⋊(ΓL(1,𝔽8)⋊D71), D3×D1491, … |
| maximal normal subgroup of | C2×C3⋊(ΓL(1,𝔽8)⋊D71), C2×C3×D1491, C2×C3⋊(C7⋊(D71⋊C5)), … |
| maximal quotient of | C2×D4473, D3×D1491, C2×C3⋊D1491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5964, 44);