Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92536 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#92536 |
| Fitting | C4×C5×C25 ⋊ C4 |
| derived, Sylow | C5×C25 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92536 |
| commutator, hypocenter | C5×C25 | C42 |
| Frattini | C2×C5 | C2×#1043 |
| Fitting | C4×C5×C25 | C4 |
| socle | C2×C52 | C2×AGL(1,𝔽5) |
| prime radical, cosocle | C2×C5⋊D25 | C22 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C4 | |
210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 500 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 325);