Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D73 |
| unambiguous semidirect product | (D5×C73)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D73)⋊(C2×C5) |
| unambiguous semidirect product | D365⋊(C2×C5) |
| Fitting, socle, Hall | C52×C73 ⋊ C22 |
| derived | C5×C73 ⋊ C22×C5 |
| Sylow | C73 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D73 |
| commutator, hypocenter | C5×C73 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C73 | C22 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
760 conjugacy classes — view the full character table.
| maximal subgroup of | D73×#3874, C5×D5×D73⋊C3, C3×C5×D5×D73, … |
| maximal normal subgroup of | C5×D5×D73⋊C3, C3×C5×D5×D73 |
| maximal quotient of | C3×C5×D5×D73, C5×D15×D73, C5×D5×D219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 29);