Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×C52×C4⋊C4 |
| unambiguous semidirect product | C4⋊(C3×C4×C52) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C52 | C22 |
| commutator | C2 | C2×C3×C4×C52 |
| Frattini, cosocle | C22 | C22×C3×C52 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C52 ◁ G | |
208 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 1200 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3)(4,5,6,7,8)(15,17)(18,19,20,21);(9,10,11,12,13)(14,15,16,17)750 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 467);