Finite Group DatabasebetaFinite Group Databasebeta| order | 37023 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C41×C43 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C41×C43 |
| unambiguous semidirect product | C7⋊(C3×C41×C43) |
| unambiguous semidirect product | (C7×C41)⋊(C3×C43) |
| Fitting, socle, Hall | C7×C41×C43 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C41×C43 |
| Hall | C7×C43 ⋊ C3×C41 |
| Hall | C7×C41 ⋊ C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41×C43 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C3×C41×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C41×C43 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C41×C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12341 |
8815 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37023, 4);