Finite Group DatabasebetaFinite Group Databasebeta| order | 37842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D1113 |
| unambiguous semidirect product | C3⋊(C17×D371) |
| unambiguous semidirect product | C7⋊(C17×D159) |
| unambiguous semidirect product | C53⋊(C17×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D1113 |
| commutator, cosocle, hypocenter | C3×C7×C53 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17×C53 | C2 |
| LCS | G ▷ C3×C7×C53 | |
| UCS | C1 ◁ C17 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18921 |
9486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37842, 15);