Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | Aut(G) order 5090400 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4242 |
| direct product | C2×D2121 |
| unambiguous semidirect product | (C2×C3)⋊D707 |
| unambiguous semidirect product | (C2×C7)⋊D303 |
| unambiguous semidirect product | (C2×C101)⋊D21 |
| Fitting, socle | C2×C3×C7×C101 ⋊ C2 |
| derived, Hall | C3×C7×C101 ⋊ C22 |
| Hall | C7×C101 ⋊ C2×D3 |
| Hall | C3×C101 ⋊ C2×D7 |
| Sylow | C101 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D101 |
| Sylow | C7 ⋊ C2×D303 |
| Sylow | C3 ⋊ C2×D707 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2121 |
| commutator, hypocenter | C3×C7×C101 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C101 | C2 |
| LCS | G ▷ C3×C7×C101 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6363, C2×C3⋊(ΓL(1,𝔽8)⋊D101), D3×D2121, … |
| maximal normal subgroup of | C2×C3⋊(ΓL(1,𝔽8)⋊D101), C2×C3×D2121, D8484 |
| maximal quotient of | C2×D6363, D3×D2121, C2×C3×D2121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 34);