Finite Group DatabasebetaFinite Group Databasebeta| order | 37604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×C7⋊#595 |
| unambiguous semidirect product | C7⋊(#595×C79) |
| Fitting, socle, Hall | C7×C17×C79 ⋊ C4 |
| derived, Hall | C7×C17 ⋊ C4×C79 |
| Hall | C17×C79 ⋊ Dic7 |
| Hall | C7×C79 ⋊ #595 |
| Sylow | C17 ⋊ Dic7×C79 |
| Sylow | C7 ⋊ #595×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C7⋊#595 |
| commutator, hypocenter | C7×C17 | C4×C79 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C79 | C4 |
| prime radical | C7×D17×C79 | C2 |
| cosocle | C7×D17 | C2×C79 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C79 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9401 |
3002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37604, 14);