Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#41⋊C3 |
| unambiguous semidirect product | #41⋊(C3×C52) |
| unambiguous semidirect product | (C5×#41)⋊(C3×C5) |
| Fitting, Hall | C52×#41 ⋊ C3 |
| Sylow | #41 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C52 | A4 |
| commutator, cosocle, hypocenter | Q8 | C2×C3×C52 |
| Frattini | C2 | C2×C52×A4 |
| Fitting | C52×#41 | C3 |
| socle | C2×C52 | C2×A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C4×C52 | |
120 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, 881);