Finite Group DatabasebetaFinite Group Databasebeta| order | 37758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C29⋊(D31⋊C3) |
| unambiguous semidirect product | (C31⋊C3)⋊(C7×D29) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C29⋊(D31⋊C3) |
| commutator, cosocle, hypocenter | C29×C31 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C31 | C2×C3 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6293 |
1351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37758, 38);