Finite Group DatabasebetaFinite Group Databasebeta| order | 7540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#10596817 |
| Fitting, socle, Hall | C5×C13×C29 ⋊ C4 |
| derived, Hall | C5×C29 ⋊ C4×C13 |
| Hall | C13×C29 ⋊ Dic5 |
| Hall | C5×C13 ⋊ #1181 |
| Sylow | C29 ⋊ C13×Dic5 |
| Sylow | C5 ⋊ C13×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #10596817 |
| commutator, hypocenter | C5×C29 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C29 | C4 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7540, 33);