Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(18,19)(20,21)(22,23,29,25)(24,34,36,49)(26,40,43,32)(27,39,46,31)(28,41,45,33)(30,42,35,37)(38,52,47,50)(44,51,53,48);(22,24,29,36)(23,30,25,35)(26,42,43,37)(27,44,46,53)(28,47,45,38)(31,49,39,34)(32,50,40,52)(33,51,41,48);(19,21)(22,25,29,23)(24,35,36,30)(26,39,43,31)(27,40,46,32)(28,41,45,33)(34,37,49,42)(38,51,47,48)(44,52,53,50);(22,26)(23,31)(24,36)(25,39)(27,45)(28,46)(29,43)(30,35)(32,41)(33,40)(34,52)(37,53)(42,44)(49,50)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26838);