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×#13229 |
| 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 | |
452 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)(20,30,34,45)(21,35)(22,38,31,27)(23,41)(24,29)(25,26)(28,42)(32,46,47,40)(33,36,48,44)(37,49)(39,43);(18,20,31,26,24,34,22,39)(19,25,38,45,29,43,27,30)(21,32,44,28,37,47,36,41)(23,33,46,35,42,48,40,49);(18,21,23,25,24,37,42,43)(19,26,28,35,29,39,41,49)(20,32,33,38,34,47,48,27)(22,36,40,30,31,44,46,45)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6217);