Finite Group DatabasebetaFinite Group Databasebeta| order | 1300 |
| isoclinism | isoclinic class of D5×D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D65 |
| unambiguous semidirect product | (C5×D5)⋊D13 |
| unambiguous semidirect product | (D5×C13)⋊D5 |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C22 |
| Sylow | C52 ⋊ C2×D13 |
| Sylow | C13 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13 | C22 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C5⋊(D13⋊C3), #3874⋊D13, C3×D5×D65, … |
| maximal normal subgroup of | D5×C5⋊(D13⋊C3), C3×D5×D65, D5×C11×D65, … |
| maximal quotient of | C3×D5×D65, D5×D195, D15×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1300, 43);