Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C73 · Schur multiplier (H2) = C2 |
| direct product | D52×C73 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C73) |
| unambiguous semidirect product | (C5⋊D5)⋊(C2×C73) |
| Fitting, socle, Hall | C52×C73 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D52 |
| commutator, hypocenter | C52 | C22×C73 |
| Frattini | C1 | G |
| Fitting, socle | C52×C73 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C73 | |
48 conjugacy classes of subgroups.
1168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C73×#3874⋊C2, D52×C73⋊C3, C3×D52×C73, … |
| maximal normal subgroup of | D52×C73⋊C3, C3×D52×C73 |
| maximal quotient of | C3×D52×C73, D5×D15×C73, C73×D15⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 43);