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×#33846 |
| 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 | |
718 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)(18,19)(20,21)(22,23,27,31)(24,32,36,50)(25,37,40,53)(26,41,39,29)(28,43,45,34)(30,47,49,38)(33,46,51,44)(35,52,42,48);(22,24)(23,28)(25,33)(26,42)(27,36)(29,46)(30,48)(31,45)(32,37)(34,38)(35,39)(40,51)(41,44)(43,47)(49,52)(50,53);(19,21);(23,29)(24,33)(25,38)(26,39)(28,32)(30,49)(31,41)(34,35)(36,51)(40,47)(42,43)(44,52)(45,50)(46,48)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26834);