Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#1830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #381 |
| commutator | C23 | C22×C4×C11 |
| Frattini, cosocle | C22×C4 | C23×C11 |
| prime radical | C23×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,20,30,35)(14,22,24,36,25,18,29,32)(15,26,28,40,27,19,33,34)(23,31,39,42,38,37,41,43);(12,14,17,25)(13,18,20,22)(15,23,27,38)(16,29,30,24)(19,31,26,37)(21,36,35,32)(28,41,33,39)(34,43,40,42);(12,15)(13,19,20,26)(14,23)(16,28)(17,27)(18,31,22,37)(21,34,35,40)(24,39)(25,38)(29,41)(30,33)(32,42,36,43)319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 562);