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×#33851 |
| 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 | |
674 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)(23,28)(24,32)(25,37)(26,40)(29,33)(30,49)(31,45)(35,36)(38,42)(39,51)(41,43)(44,50)(47,53)(48,52);(22,23,27,31)(24,33,36,52)(25,38,41,49)(26,42,40,30)(28,43,45,37)(29,46,48,34)(32,44,35,53)(39,50,51,47);(19,21);(22,24,27,36)(23,29,31,48)(25,39,41,51)(26,32,40,35)(28,44,45,53)(30,50,42,47)(33,49,52,38)(34,43,46,37)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26839);