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×#33853 |
| 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 | |
696 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)(24,33)(25,34)(26,35)(29,40)(30,36)(31,46)(32,44)(38,39)(41,51)(42,43)(45,50)(47,53)(49,52);(22,23,27,31)(24,29,33,32)(25,36,38,52)(26,40,42,44)(28,43,46,35)(30,48,49,37)(34,45,39,53)(41,50,51,47);(19,21)(22,24,27,33)(23,29,31,32)(25,34,38,39)(26,35,42,43)(28,44,46,40)(30,47,49,50)(36,45,52,53)(37,51,48,41);(22,25,27,38)(23,30,31,49)(24,34,33,39)(26,41,42,51)(28,45,46,53)(29,47,32,50)(35,37,43,48)(36,44,52,40)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26841);