Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#23472 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#393 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,25)(21,33,35,44)(22,27)(23,38)(24,28)(26,36,43,37)(29,42,45,49)(30,40)(31,41)(32,47)(34,39,46,48);(18,20)(19,25)(21,34,35,46)(22,31)(23,32)(24,30)(26,42,43,49)(27,41)(28,40)(29,37,45,36)(33,48,44,39)(38,47);(18,21)(19,26)(20,29)(22,37)(23,36)(24,35)(25,39)(27,44)(28,43)(30,45)(31,34)(32,46)(33,38)(40,48)(41,49)(42,47);(20,30)(25,40)(29,45)(31,32)(34,46)(39,48)(41,47)(42,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16460);