Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C4×C5×GL(3,𝔽2) (order 3360) · Inn(G) = C1 · Out(G) = C4×C5×GL(3,𝔽2) |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C25 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5 | C23×C5 |
| socle, prime radical | C23×C5 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 14);