Finite Group DatabasebetaFinite Group Databasebeta| order | 37142 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D7×C379⋊C7 |
| unambiguous semidirect product | C7⋊(C2×C379⋊C7) |
| unambiguous semidirect product | (D7×C379)⋊C7 |
| Fitting, socle, derived | C7×C379 ⋊ C2×C7 |
| Hall | C7×C379⋊C7 ⋊ C2 |
| Sylow | C379 ⋊ C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C379 | C2×C7 |
| LCS | G ▷ C7×C379 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2653 |
305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37142, 10);