Finite Group DatabasebetaFinite Group Databasebeta| order | 21042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D21×C167 |
| unambiguous semidirect product | C3⋊(D21×C167) |
| unambiguous semidirect product | C7⋊(C3⋊D3×C167) |
| Fitting, socle, Hall | C32×C7×C167 ⋊ C2 |
| derived, Hall | C32×C7 ⋊ C2×C167 |
| Hall | C32×C167 ⋊ D7 |
| Hall | C7×C167 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D7×C167 |
| Sylow | C7 ⋊ C3⋊D3×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | C3⋊D21 |
| commutator, cosocle, hypocenter | C32×C7 | C2×C167 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C167 | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C167 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10521 |
5511 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21042, 31);