Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C52 |
| direct product | C52×C5⋊D5 |
| unambiguous semidirect product | C5⋊(C52×D5) |
| Fitting, socle, Sylow | C54 ⋊ C2 |
| derived | C52 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C54 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C52 | |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#92566, C5×C5⋊#3874, C5⋊D52, … |
| maximal normal subgroup of | C5×#92566, C5⋊D52, C52×D52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 53);