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×#3563 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| prime radical | C11×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
912 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)(14,21)(15,18)(16,24)(17,20)(19,25)(22,26)(23,27)(28,29,34,37)(30,32,35,31)(33,41,42,36)(38,39,43,40);(12,14,17,15)(13,18,20,21)(16,22,25,23)(19,26,24,27)(28,30,34,35)(29,31,37,32)(33,38,42,43)(36,39,41,40);(12,15,17,14)(13,18,20,21)(16,23,25,22)(19,26,24,27)(28,31,34,32)(29,35,37,30)(33,39,42,40)(36,43,41,38);(12,13)(14,21)(15,18)(16,19)(17,20)(22,27)(23,26)(24,25)(28,32,34,31)(29,30,37,35)(33,40,42,39)(36,38,41,43);(12,16)(13,19)(14,22)(15,23)(17,25)(18,26)(20,24)(21,27)(28,33)(29,36)(30,38)(31,39)(32,40)(34,42)(35,43)(37,41)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2295);