Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #1043⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C4×#1043⋊C5 |
| unambiguous semidirect product | (C4×#1043)⋊C5 |
| Fitting | C4×H(3,𝔽5) ⋊ C4 |
| derived | C52 ⋊ C42×C5 |
| Sylow | H(3,𝔽5) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #1043⋊C5 |
| commutator, hypocenter | C52 | C42×C5 |
| Frattini, socle | C2×C5 | C2×C5×AGL(1,𝔽5) |
| Fitting | C4×H(3,𝔽5) | C4 |
| prime radical | C2×(C5⋊D5)⋊C5 | C22 |
| cosocle | C2×C5⋊D5 | C22×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(#1043⋊C5)⋊C2 |
| maximal normal subgroup of | C4×(#1043⋊C5)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 284);