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×#3565 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,17)(14,20,21,18)(15,23,24,19)(22,25,27,26)(28,29)(30,35)(31,36)(32,40)(33,34)(37,41)(38,39)(42,43);(13,17)(14,21)(19,23)(22,27)(29,34)(31,35)(37,40)(39,42);(12,14,16,21)(13,18,17,20)(15,22,24,27)(19,25,23,26)(28,30,33,36)(29,35,34,31)(32,38,41,43)(37,42,40,39);(12,13)(14,18)(15,19)(16,17)(20,21)(22,25)(23,24)(26,27)(28,31,33,35)(29,36,34,30)(32,39,41,42)(37,43,40,38);(12,15,16,24)(13,19,17,23)(14,22,21,27)(18,25,20,26)(28,32,33,41)(29,37,34,40)(30,38,36,43)(31,39,35,42)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2297);