Finite Group DatabasebetaFinite Group Databasebeta| order | 24025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C31⋊C25 |
| unambiguous semidirect product | C31⋊(C25×C31) |
| derived | C31 ⋊ C25×C31 |
| Sylow | C312 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C31 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C25×C31 |
| Frattini | C5 | C31×ΓL(1,𝔽32) |
| Fitting, socle, prime radical | C5×C312 | C5 |
| cosocle | C5×C31 | C5×C31 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 775 |
1705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24025, 6);