Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20892 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#120 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#385 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,23,26,33,39)(20,24,30,36,29,35,43,47)(21,25,32,38,31,37,44,48)(28,40,42,49,41,34,45,46);(18,20,22,30,23,29,33,43)(19,24,27,36,26,35,39,47)(21,28,32,42,31,41,44,45)(25,34,38,46,37,40,48,49);(18,21)(19,25)(20,28)(22,32)(23,31)(24,34)(26,37)(27,38)(29,41)(30,42)(33,44)(35,40)(36,46)(39,48)(43,45)(47,49);(19,26)(24,35)(25,37)(27,39)(34,40)(36,47)(38,48)(46,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13880);