Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25435 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×#41×C17 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
880 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)(18,19,21,20)(22,23,29,34)(24,35,25,31)(26,40,43,53)(27,44,28,33)(30,39,46,37)(32,42,48,41)(36,50,38,45)(47,51,49,52);(18,20,21,19)(22,24,28,39,29,25,27,37)(23,30,44,31,34,46,33,35)(26,36,42,52,43,38,41,51)(32,45,53,47,48,50,40,49);(19,20)(22,25)(23,31)(24,29)(26,38)(27,39)(28,37)(30,33)(32,47)(34,35)(36,43)(40,45)(41,52)(42,51)(44,46)(48,49)(50,53);(22,26,28,42,29,43,27,41)(23,32,44,53,34,48,33,40)(24,36,39,52,25,38,37,51)(30,45,31,47,46,50,35,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18423);