Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C4 |
| direct product | C11×#2245 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ C4×C8×C11 ◁ G | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,27,33)(22,29,37,48)(23,28,39,46)(24,31,41,43)(25,30,34,49)(26,42,40,32)(35,47,50,45)(36,51,38,44);(13,16)(17,19)(20,22,34,50,26,36,24,23,27,37,25,35,40,38,41,39)(21,28,43,51,32,45,30,29,33,46,31,44,42,47,49,48);(12,14,15,18)(13,17,16,19)(20,23,24,38,40,50,34,37,27,39,41,36,26,35,25,22)(21,29,30,47,42,51,43,46,33,48,49,45,32,44,31,28)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 977);