Finite Group DatabasebetaFinite Group Databasebeta| order | 25265 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C163 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×C163 |
| unambiguous semidirect product | C31⋊(C5×C163) |
| unambiguous semidirect product | (C31×C163)⋊C5 |
| Fitting, socle, Hall | C31×C163 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C163 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C163 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C163 |
| Frattini | C1 | G |
| Fitting, socle | C31×C163 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C163 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5053 |
1793 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25265, 1);