Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D303 |
| unambiguous semidirect product | (C2×C3)⋊(C7×D101) |
| unambiguous semidirect product | (C2×C101)⋊(D3×C7) |
| Fitting, socle | C2×C3×C7×C101 ⋊ C2 |
| derived, Hall | C3×C101 ⋊ C22×C7 |
| Hall | C3×C7×C101 ⋊ C22 |
| Hall | C7×C101 ⋊ C2×D3 |
| Sylow | C101 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ C2×D101 |
| Sylow | C3 ⋊ C2×C7×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D303 |
| commutator, hypocenter | C3×C101 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C101 | C2 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
2142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×D909, C2×ΓL(1,𝔽8)×D303, D3×C7×D303, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D303, C2×C3×C7×D303 |
| maximal quotient of | C2×C7×D909, D3×C7×D303, C2×C3×C7×D303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 36);