Finite Group DatabasebetaFinite Group Databasebeta| order | 25625 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C52 |
| direct product | 5−1+2×C41⋊C5 |
| Fitting | C41×5−1+2 ⋊ C5 |
| Sylow | C41 ⋊ C5×5−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C52×C41⋊C5 |
| commutator, socle, cosocle | C5×C41 | C53 |
| Fitting | C41×5−1+2 | C5 |
| prime radical | C52×C41⋊C5 | C5 |
| hypercenter | 5−1+2 | C41⋊C5 |
| hypocenter | C41 | C5×5−1+2 |
| LCS | G ▷ C5×C41 ▷ C41 | |
| UCS | C1 ◁ C5 ◁ 5−1+2 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1025 |
377 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25625, 50);