Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4×C5 |
| direct product | C4×#1039⋊C5 |
| unambiguous semidirect product | (C4×#1039)⋊C5 |
| derived | C52 ⋊ C42×C5 |
| Sylow | H(3,𝔽5) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | (C5⋊D5)⋊C5 |
| commutator, hypocenter | C52 | C42×C5 |
| Frattini, socle | C22×C5 | C2×C5×D5 |
| Fitting | C2×C4×H(3,𝔽5) | C2 |
| prime radical | C22×H(3,𝔽5) | C22 |
| cosocle | C22×C52 | C22×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
137 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 148);