Finite Group DatabasebetaFinite Group Databasebeta| order | 2325 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C5×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C3×C31)⋊C52 |
| unambiguous semidirect product | (C3×C5×C31)⋊C5 |
| Fitting, socle | C3×C5×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C3×C52 |
| Hall | C3×C31 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 465 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2325, 7);