Finite Group DatabasebetaFinite Group Databasebeta| order | 2500 |
| isoclinism | isoclinic class of #1043⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#1043⋊C5 |
| Fitting, Sylow | C5×H(3,𝔽5) ⋊ C4 |
| derived | C52 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #1043⋊C5 |
| commutator, hypocenter | C52 | C4×C52 |
| Frattini | C5 | C52×AGL(1,𝔽5) |
| Fitting | C5×H(3,𝔽5) | C4 |
| socle | C52 | C5×AGL(1,𝔽5) |
| prime radical | C5×(C5⋊D5)⋊C5 | C2 |
| cosocle | C5⋊D5 | C2×C52 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C5 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #72229811, #72229817 |
Past the SmallGroups library coverage — no SmallGroups id.