Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33426 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#117 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C8 | C24×C17 |
| socle | C2×C17 | C2×#432 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C17×#97 ◁ G | |
520 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)(18,19,21,27,22,28,35,44,23,26,34,42,36,25,40,41)(20,29,31,43,32,37,46,48,30,24,33,38,45,39,47,49);(18,20)(19,24)(21,33)(22,32)(23,30)(25,37)(26,29)(27,43)(28,39)(31,34)(35,47)(36,45)(38,42)(40,46)(41,49)(44,48);(19,25,26,28)(21,34)(24,37,29,39)(27,44,42,41)(31,33)(35,40)(38,49,43,48)(46,47);(20,30)(24,29)(31,33)(32,45)(37,39)(38,43)(46,47)(48,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26414);