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×#3568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
958 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)(12,13,17,19)(14,23,27,25)(15,18,22,28)(16,30,31,21)(20,34,33,24)(26,39,40,37)(29,41,36,32)(35,38,42,43);(13,19)(14,24)(15,22)(20,25)(21,30)(23,33)(26,38)(27,34)(29,36)(35,39)(37,42)(40,43);(12,14,17,27)(13,20,19,33)(15,25,22,23)(16,26,31,40)(18,24,28,34)(21,35,30,42)(29,39,36,37)(32,38,41,43);(12,15,28,13)(14,25,34,20)(16,29,41,21)(17,22,18,19)(23,24,33,27)(26,39,43,35)(30,31,36,32)(37,38,42,40);(12,16,28,41)(13,21,15,29)(14,26,34,43)(17,31,18,32)(19,30,22,36)(20,35,25,39)(23,37,33,42)(24,38,27,40)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2300);