Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10757 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | C22⋊#95 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1168 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)(18,19,22,28,24,27,23,36)(20,25,31,39,30,38,35,40)(21,26,33,41,32,42,34,47)(29,43,45,49,44,37,46,48);(18,20,23,31,24,30,22,35)(19,25,28,40,27,38,36,39)(21,29,34,45,32,44,33,46)(26,37,41,49,42,43,47,48);(18,21)(19,26)(20,29)(22,33)(23,34)(24,32)(25,37)(27,42)(28,41)(30,44)(31,45)(35,46)(36,47)(38,43)(39,48)(40,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3745);