Finite Group DatabasebetaFinite Group Databasebeta| order | 36260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×C7⋊#3866 |
| unambiguous semidirect product | C7⋊(C5×C7×#3866) |
| Fitting, socle, Hall | C5×C72×C37 ⋊ C4 |
| derived | C7×C37 ⋊ C4×C5×C7 |
| Hall | C72×C37 ⋊ C4×C5 |
| Hall | C5×C72 ⋊ #3866 |
| Hall | C5×C37 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ C5×#3866 |
| Sylow | C37 ⋊ C5×C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C7⋊#3866 |
| commutator, hypocenter | C7×C37 | C4×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C37 | C4 |
| prime radical | C5×C72×D37 | C2 |
| cosocle | C7×D37 | C2×C5×C7 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C5×C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2590 |
2555 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36260, 53);