Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1869 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C8×C17 ◁ G | |
456 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)(18,19,24,29,23,28,42,46,25,30,44,48,22,41,32,33)(20,31,35,49,36,21,38,40,37,39,27,47,34,26,45,43);(18,20,32,45,22,34,44,27,25,37,42,38,23,36,24,35)(19,26,46,49,41,39,29,43,30,21,33,47,28,31,48,40);(18,21)(19,27)(20,33)(22,31)(23,39)(24,43)(25,26)(28,45)(29,36)(30,35)(32,47)(34,48)(37,46)(38,41)(40,44)(42,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5974);