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×#25433 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
916 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)(22,23,27,33)(24,29,37,45)(25,38,41,47)(26,32,39,31)(28,36,43,35)(30,46,48,40)(34,49,52,42)(44,51,53,50);(18,20,21,19)(22,24,26,35,27,37,39,36)(23,28,31,29,33,43,32,45)(25,34,40,50,41,52,46,51)(30,42,38,44,48,49,47,53);(19,20)(22,24)(23,29)(25,34)(26,35)(27,37)(28,32)(30,44)(31,43)(33,45)(36,39)(38,49)(40,50)(41,52)(42,47)(46,51)(48,53);(22,25,39,46,27,41,26,40)(23,30,32,47,33,48,31,38)(24,34,36,51,37,52,35,50)(28,42,45,53,43,49,29,44)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18421);