Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×D25 |
| unambiguous semidirect product | C25⋊(C2×SL(2,𝔽3)) |
| unambiguous semidirect product | (Q8×D25)⋊C3 |
| Fitting, derived | Q8×C25 ⋊ C2×C3 |
| Hall | Q8×D25 ⋊ C3 |
| Sylow | C25 ⋊ C2×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×D25 |
| commutator, Fitting, cosocle, hypocenter | Q8×C25 | C2×C3 |
| Frattini, socle | C2×C5 | D5×A4 |
| LCS | G ▷ Q8×C25 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 103);