Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C101 · Schur multiplier (H2) = C1 |
| direct product | Dic21×C101 |
| unambiguous semidirect product | C3⋊(Dic7×C101) |
| unambiguous semidirect product | C7⋊(Dic3×C101) |
| derived, Hall | C3×C7 ⋊ C4×C101 |
| Hall | C3×C7×C101 ⋊ C4 |
| Hall | C7×C101 ⋊ Dic3 |
| Hall | C3×C101 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic3×C101 |
| Sylow | C3 ⋊ Dic7×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C101 | D21 |
| commutator, hypocenter | C3×C7 | C4×C101 |
| Frattini | C2 | D21×C101 |
| Fitting, socle | C2×C3×C7×C101 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C101 | |
24 conjugacy classes of subgroups.
2424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×Dic63, C101×C3⋊(ΓL(1,𝔽8)⋊C4), C101×C3⋊Dic21, … |
| maximal normal subgroup of | C101×C3⋊(ΓL(1,𝔽8)⋊C4), C3×Dic21×C101 |
| maximal quotient of | C101×Dic63, C101×C3⋊Dic21, C3×Dic21×C101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 8);