Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1893 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ 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)(18,19,23,28,25,21,24,36)(20,29,33,45,34,46,32,44)(22,37,38,35,40,49,39,27)(26,41,43,48,30,47,42,31);(18,20,22,31,23,33,38,41,25,34,40,48,24,32,39,47)(19,26,35,46,36,42,37,45,21,30,27,29,28,43,49,44);(18,21)(19,25)(20,30)(22,27)(23,28)(24,36)(26,34)(29,31)(32,42)(33,43)(35,40)(37,39)(38,49)(41,44)(45,47)(46,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6058);