Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#2166 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #117 |
| commutator | C2×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C8 | C23×C11 |
| socle | C2×C11 | #432 |
| prime radical | C23×C11 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C11×#97 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,21,16,22,29,38,17,20,28,36,30,19,33,35)(14,23,25,37,26,34,40,43,24,18,27,32,39,31,41,42);(12,14)(13,18)(15,27)(16,26)(17,24)(19,34)(20,23)(21,37)(22,31)(25,28)(29,41)(30,39)(32,36)(33,40)(35,42)(38,43);(13,19,20,22)(14,24)(15,28)(18,31,23,34)(21,38,36,35)(26,39)(29,33)(32,43,37,42)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 898);