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×#3566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
954 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)(13,19)(14,24)(15,29)(16,32)(20,37)(21,27)(23,36)(25,35)(28,41)(30,38)(31,42)(33,43);(12,13)(14,25)(15,30)(16,22)(17,19)(18,23)(20,24)(21,31)(26,32)(27,29)(28,37)(33,39)(34,36)(35,41)(38,42)(40,43);(12,14,17,28)(13,20,19,35)(15,26,31,22)(16,27,32,38)(18,24,34,41)(21,33,30,43)(23,25,36,37)(29,40,42,39);(12,15)(13,21)(14,26)(16,25)(17,31)(18,29)(19,30)(20,33)(22,28)(23,38)(24,40)(27,36)(32,37)(34,42)(35,43)(39,41);(12,16,18,33)(13,22,23,39)(14,27,24,30)(15,25,29,20)(17,32,34,43)(19,26,36,40)(21,28,38,41)(31,37,42,35)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2298);