Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
406 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)(19,25)(20,29)(21,23)(22,36)(26,42)(27,37)(28,34)(30,45)(31,38)(32,47)(33,46)(35,39)(40,44)(43,48);(18,19)(20,30)(21,34)(22,37)(23,25)(24,28)(26,32)(27,39)(29,44)(31,43)(33,40)(35,41)(36,49)(38,45)(42,46)(47,48);(18,20)(19,26,28,30)(21,33)(22,38)(23,31)(24,32)(25,40,34,43)(27,45,37,42)(29,36)(35,47)(39,46)(41,44,49,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6392);