Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13291 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#13291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1993 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
306 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)(20,31,35,47)(21,37,40,45)(22,41)(23,28)(24,30)(25,26,39,44)(27,32)(29,43)(33,42)(34,38,36,49)(46,48);(18,20,32,45,43,34,22,26,24,35,48,37,23,36,42,44)(19,25,33,49,28,40,46,47,30,39,41,38,29,21,27,31);(18,21,24,40)(19,26)(20,33)(22,38,42,49)(23,39,43,25)(27,36)(28,37)(29,45)(30,44)(31,32,47,48)(34,46)(35,41)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6279);