Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13197 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #121 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1954 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,30,24,29,40,45,25,31,39,27,22,28,21,38)(20,32,36,48,34,44,33,47,37,46,41,49,35,26,42,43);(18,20,21,33,22,35,39,36,25,37,40,42,24,34,23,41)(19,26,38,48,28,46,27,43,31,44,45,49,29,32,30,47);(18,21,22,39,25,40,24,23)(19,27,29,38,31,30,28,45)(20,33,35,36,37,42,34,41)(26,43,32,48,44,47,46,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6185);