Finite Group DatabasebetaFinite Group Databasebeta| order | 7450 |
| isoclinism | isoclinic class of D149 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D149 |
| unambiguous semidirect product | C149⋊(C2×C52) |
| Fitting, socle, Hall | C52×C149 ⋊ C2 |
| derived, Sylow | C149 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D149 |
| commutator, hypocenter | C149 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C149 | C2 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
1900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#10597010, C5×#15688384, C5×D5×D149, … |
| maximal normal subgroup of | C52×#10597010, C5×#15688384, C5×D5×D149, … |
| maximal quotient of | C52×Dic149, C2×C52×D149, C3×C52×D149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7450, 6);