Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D5×#1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | D5×#1044 |
| Fitting, socle, derived, Sylow | C53 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C2×C4 |
| prime radical | D5×C5⋊D5 | C2 |
| cosocle | C5×C5⋊D5 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1044, #14522937, #14522943, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1044, #14522937, #14522943, … |
| maximal quotient of | Dic5×#1044, #14522700, #14522701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 171);