Finite Group DatabasebetaFinite Group Databasebeta| order | 24025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C961⋊C25 |
| derived, Sylow | C961 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C961⋊C5 |
| commutator, hypocenter | C961 | C25 |
| Frattini, socle, prime radical | C5×C31 | ΓL(1,𝔽32) |
| Fitting, cosocle | C5×C961 | C5 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C5 | |
9 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24025 |
Polycyclic presentation:
5,31,5,31|a^5=c,b^31=d^13,b^a=b^16d,d^a=d^16985 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24025, 2);