Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×#1042 |
| unambiguous semidirect product | D5⋊(C5×Dic5) |
| Fitting, socle | C2×C53 ⋊ C4 |
| derived | C52 ⋊ C2×C4×C5 |
| Sylow | C53 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #1042 |
| commutator, hypocenter | C52 | C2×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C4 |
| prime radical | C2×C52×D5 | C2 |
| cosocle | C5×D5 | C22×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C5 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 187);