Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10905 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1436 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
672 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)(18,19,23,27,24,28,22,37)(20,29,32,41,33,40,31,25)(21,34,35,26,36,42,38,43)(30,45,46,49,48,39,47,44);(18,20)(19,25,28,41)(21,30)(22,31)(23,32)(24,33)(26,39,43,45)(27,29,37,40)(34,49,42,44)(35,46)(36,48)(38,47);(18,21,23,35,24,36,22,38)(19,26,27,42,28,43,37,34)(20,30,32,46,33,48,31,47)(25,39,29,44,41,45,40,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3893);