Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#1840 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C23 |
| commutator | C23 | C22×C4×C11 |
| Frattini, cosocle | C22×C4 | C23×C11 |
| socle, prime radical | C23×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,19)(15,17)(16,18)(20,21)(22,24)(23,25)(26,27)(28,29,31,34,32,35,38,41)(30,33,37,40,36,39,42,43);(12,14,16,15)(13,17,18,19)(20,22,23,26)(21,24,25,27)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(12,15,16,14)(13,17,18,19)(21,25)(24,27)(30,36)(33,39)(37,42)(40,43)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 572);