Finite Group DatabasebetaFinite Group Databasebeta| order | 1300 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D52×C13 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C13) |
| unambiguous semidirect product | (C5⋊D5)⋊(C2×C13) |
| Fitting, socle, Hall | C52×C13 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D52 |
| commutator, cosocle, hypocenter | C52 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | D52×C13⋊C3, C13×#3874⋊C2, C3×D52×C13, … |
| maximal normal subgroup of | D52×C13⋊C3, C3×D52×C13, D52×C11×C13, … |
| maximal quotient of | C3×D52×C13, D5×C13×D15, C13×D15⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1300, 42);