Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11031 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1262 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)(24,33)(25,38,41,30)(26,42)(27,31)(28,32)(29,35)(34,46,51,50)(36,45)(37,49)(39,53,52,44)(40,47,43,48);(19,21)(22,24,28,37)(23,29,32,45)(25,39,41,52)(26,36,27,35)(30,46,38,50)(31,49,42,33)(34,43,51,40)(44,47,53,48);(22,25)(23,30)(24,34)(26,40)(27,43)(28,41)(29,44)(31,47)(32,38)(33,50)(35,39)(36,52)(37,51)(42,48)(45,53)(46,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4019);