Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#3564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| prime radical | C11×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,23,19)(15,26,29,20)(16,18,28,32)(24,34,36,35)(25,33,37,30)(27,40,41,31)(38,43,39,42);(13,18)(14,23)(15,27)(19,33)(21,32)(22,30)(24,38)(25,37)(29,41)(34,35)(36,39)(42,43);(12,14,16,25)(13,19,18,30)(15,24,27,39)(17,23,28,37)(20,34,31,42)(21,22,32,33)(26,35,40,43)(29,36,41,38);(12,15,28,41)(13,20,32,40)(14,24,37,38)(16,27,17,29)(18,31,21,26)(19,34,33,43)(22,35,30,42)(23,36,25,39);(13,18)(19,30)(20,31)(21,32)(22,33)(26,40)(34,42)(35,43)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2296);