Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#10951 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1437 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
916 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)(20,24,29,39)(21,31)(22,34)(23,26)(25,33)(27,36)(28,42,44,45)(30,41,35,38)(32,46)(37,48,49,43)(40,47);(18,20)(19,24,26,39)(21,28)(22,35)(23,29)(25,37,40,49)(27,41,34,38)(30,36)(31,45,46,42)(32,44)(33,48)(43,47);(18,21,22,33,23,32,36,47)(19,25,27,31,26,40,34,46)(20,28,35,48,29,44,30,43)(24,37,41,45,39,49,38,42)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3939);