Finite Group DatabasebetaFinite Group Databasebeta| order | 25625 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C52 |
| unambiguous semidirect product | C52⋊(C41⋊C25) |
| Sylow | C41 ⋊ C52⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C52 | C5×C41⋊C5 |
| commutator | C5×C41 | C5×C25 |
| Fitting, prime radical | C53×C41 | C5 |
| socle, cosocle | C52×C41 | C52 |
| hypercenter | C53 | C41⋊C5 |
| hypocenter | C41 | C52⋊C25 |
| LCS | G ▷ C5×C41 ▷ C41 | |
| UCS | C1 ◁ C52 ◁ C53 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5125 |
Polycyclic presentation:
5^4,41|a^5=d,b^a=bc,e^a=e^101145 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25625, 19);