Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C53 |
| direct product | C53×D5 |
| unambiguous semidirect product | C5⋊(C2×C53) |
| Fitting, socle, Sylow | C54 ⋊ C2 |
| derived | C5 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C54 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C53 | |
752 conjugacy classes of subgroups.
| transitive degree | μt(G) = 250 |
500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D52, C5×D5×C5⋊D5, D5×C5⋊(C5⋊D5) |
| maximal normal subgroup of | C52×D52, C5×D5×C5⋊D5, D5×C5⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 52);