Finite Group DatabasebetaFinite Group Databasebeta| order | 25625 |
| automorphism | ? |
| homology | Abelianization (H1) = C252 · Schur multiplier (H2) = C25 |
| direct product | C25×C41⋊C25 |
| unambiguous semidirect product | C41⋊C252 |
| derived, Sylow | C41 ⋊ C252 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C25 | C41⋊C5 |
| commutator, hypocenter | C41 | C252 |
| Frattini | C52 | C5×C41⋊C5 |
| Fitting | C5×C25×C41 | C5 |
| socle, prime radical, cosocle | C52×C41 | C52 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C5×C25 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25625 |
1625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25625, 17);