Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic303 |
| unambiguous semidirect product | C3⋊(C7×Dic101) |
| derived, Hall | C3×C101 ⋊ C4×C7 |
| Hall | C3×C7×C101 ⋊ C4 |
| Hall | C7×C101 ⋊ Dic3 |
| Sylow | C101 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ Dic101 |
| Sylow | C3 ⋊ C7×Dic101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D303 |
| commutator, hypocenter | C3×C101 | C4×C7 |
| Frattini | C2 | C7×D303 |
| Fitting, socle | C2×C3×C7×C101 | C2 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
2142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×Dic909, ΓL(1,𝔽8)×Dic303, C7×C3⋊Dic303, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×Dic303, C3×C7×Dic303 |
| maximal quotient of | C7×Dic909, C7×C3⋊Dic303, C3×C7×Dic303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 7);