Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D301 |
| derived, Hall | C72×C43 ⋊ C2×C9 |
| Hall | C7×C43×C7⋊C9 ⋊ C2 |
| Hall | C7×D301 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ D43 |
| Sylow | C72 ⋊ C9×D43 |
| Sylow | C43 ⋊ D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D301 |
| commutator, hypocenter | C72×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C43 | C2×C3 |
| prime radical | C3×C7×D301 | C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5418 |
2280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 164);