Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#2103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C11 |
| socle | C2×C11 | #400 |
| prime radical | C23×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
148 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)(12,13,16,21,17,22,18,33)(14,23,25,35,27,38,26,19)(15,28,30,42,31,20,32,37)(24,36,39,43,40,41,29,34);(12,14,18,25,17,27,16,26)(13,19,33,23,22,35,21,38)(15,29,32,24,31,39,30,40)(20,36,42,43,28,41,37,34);(12,15,16,30,17,31,18,32)(13,20,21,37,22,28,33,42)(14,24,25,39,27,40,26,29)(19,34,23,36,35,43,38,41)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 835);