Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#1745 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C23 |
| commutator | C22 | C2×C42×C11 |
| Frattini, cosocle | C22×C4 | C23×C11 |
| socle, prime radical | C23×C11 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
272 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,21)(19,20)(22,23)(24,25,26,29,27,28,30,31);(12,13,14,15)(17,20)(21,23);(16,18,19,22)(17,21,20,23)(25,28)(29,31)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 477);