Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13394 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,29,35)(24,36,39,48)(25,40,37,30)(26,34,28,32)(27,43,46,52)(31,49,51,41)(33,42,53,45)(38,50,44,47);(18,19)(20,21)(22,24)(23,30)(25,26)(27,44)(28,37)(29,39)(31,43)(32,48)(33,50)(34,36)(35,40)(38,46)(41,45)(42,49)(47,53)(51,52);(19,21)(22,25,26,24,29,37,28,39)(23,31,32,47,35,51,34,50)(27,44,42,41,46,38,45,49)(30,33,36,52,40,53,48,43)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6382);