Finite Group DatabasebetaFinite Group Databasebeta| order | 37932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#89137⋊C3 |
| unambiguous semidirect product | #89137⋊(C3×C29) |
| unambiguous semidirect product | (C29×#89137)⋊C3 |
| Fitting, socle, Hall | C29×C109 ⋊ C3×C4 |
| derived, Sylow | C109 ⋊ C3×C4×C29 |
| Hall | C29×#89137 ⋊ C3 |
| Hall | C29×C109⋊C3 ⋊ C4 |
| Hall | #89137 ⋊ C3×C29 |
| Hall | C109⋊C3 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #89137⋊C3 |
| commutator, hypocenter | C109 | C3×C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C109 | C3×C4 |
| prime radical | C29×D109⋊C3 | C2 |
| cosocle | D109 | C2×C3×C29 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3161 |
609 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37932, 14);