Finite Group DatabasebetaFinite Group Databasebeta| order | 37503 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C33×C463⋊C3 |
| unambiguous semidirect product | C463⋊C34 |
| unambiguous semidirect product | (C3×C463)⋊C33 |
| Fitting, socle | C33×C463 ⋊ C3 |
| derived, Sylow | C463 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C463⋊C3 |
| commutator, cosocle, hypocenter | C463 | C34 |
| Frattini | C1 | G |
| Fitting, socle | C33×C463 | C3 |
| LCS | G ▷ C463 | |
| UCS | C1 ◁ C33 | |
424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12501 |
4239 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37503, 49);