Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C5 |
| abelian | C2×C52×C8 |
| multiplicative | (ℤ/451)ˣ, (ℤ/902)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C52 |
| socle, prime radical | C22×C52 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5,6,7,8)(11,12,13,14,15);(9,10)(16,17,18,19,20)400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 111);