Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24805 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#24807 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,29,33,28,35,27,34)(24,36,45,32,26,44,38,30)(25,39,41,31,43,49,42,48)(37,47,51,50,40,46,52,53);(18,19)(20,21)(22,24,27,38,28,26,29,45)(23,30,33,36,35,32,34,44)(25,37,41,51,43,40,42,52)(31,46,39,50,48,47,49,53);(19,21)(22,25)(23,31)(24,37)(26,40)(27,41)(28,43)(29,42)(30,46)(32,47)(33,39)(34,49)(35,48)(36,50)(38,51)(44,53)(45,52);(22,26,29,38,28,24,27,45)(23,32,34,36,35,30,33,44)(25,40,42,51,43,37,41,52)(31,47,49,50,48,46,39,53)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17795);