Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×#1042 |
| Fitting, socle, derived, Sylow | C53 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C42 |
| prime radical, cosocle | C5×D52 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
140 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 80 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(1,𝔽5)2 |
| maximal normal subgroup of | D5×AGL(1,𝔽5)2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 903);