Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
682 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)(23,28)(25,36)(26,37)(29,38)(30,39)(31,43)(32,42)(34,49)(35,48)(40,41)(44,47)(45,50)(46,53)(51,52);(22,23,29,43,26,31,25,28,27,32,36,41,37,40,38,42)(24,30,44,53,35,46,34,39,33,45,49,52,48,51,47,50);(19,21)(22,24)(23,30)(25,34)(26,35)(27,33)(28,39)(29,44)(31,46)(32,45)(36,49)(37,48)(38,47)(40,51)(41,52)(42,50)(43,53);(24,33)(30,45)(34,47)(35,48)(39,50)(44,49)(46,51)(52,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26597);