Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#41⋊C3 |
| unambiguous semidirect product | #41⋊(C3×C25) |
| unambiguous semidirect product | (#41×C25)⋊C3 |
| Fitting, Hall | #41×C25 ⋊ C3 |
| Sylow | #41 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C25 | A4 |
| commutator, hypocenter | Q8 | C2×C3×C25 |
| Frattini, socle | C2×C5 | C2×C5×A4 |
| Fitting | #41×C25 | C3 |
| prime radical | C5×#41⋊C3 | C5 |
| cosocle | C5×Q8 | C2×C3×C5 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C4×C25 | |
45 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 148);