Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13232 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1964 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×#131 ◁ G | |
448 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)(18,19,24,29,25,30,23,42)(20,31,35,38,36,46,34,49)(21,37,26,44,40,33,39,27)(22,28,32,45,41,48,43,47);(18,20,32,27)(19,26,45,38)(21,28,46,29)(22,33,24,35)(23,34,41,37)(25,36,43,44)(30,39,47,49)(31,42,40,48);(18,21,23,39,25,40,24,26)(19,27,29,37,30,44,42,33)(20,28,34,47,36,48,35,45)(22,38,32,46,41,49,43,31)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6220);