Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
422 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)(20,29)(21,34)(22,23)(25,39)(26,41)(27,38)(30,42)(31,46)(32,47)(33,35)(36,37)(40,49)(43,48)(44,45);(18,19)(20,30)(21,26)(22,38)(23,27)(24,28)(25,32)(29,45)(31,44)(33,40)(34,41)(35,39)(36,48)(37,43)(42,46)(47,49);(18,20,23,32,24,31,22,33)(19,25,27,44,28,40,38,30)(21,35,34,46,37,47,36,29)(26,42,41,49,43,45,48,39)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6384);