Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
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)(18,19)(20,21)(22,23)(24,36)(25,43)(26,33)(27,32)(28,45)(29,48)(30,35)(31,38)(34,46)(37,39)(40,52)(41,44)(42,53)(47,51)(49,50);(22,24,30,42)(23,31,35,52)(25,44,32,50)(26,39,28,47)(27,38,43,40)(29,49,46,41)(33,36,45,53)(34,37,48,51);(19,21)(22,25,26,34,46,33,43,23,30,32,28,48,29,45,27,35)(24,37,38,44,49,52,47,53,42,51,40,50,41,31,39,36)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6434);