Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25437 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
894 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)(24,29,37,46)(25,38,41,49)(26,32,42,31)(28,36,44,35)(30,47,50,40)(34,51,39,43)(45,53,48,52);(18,20,21,19)(22,24,26,35,27,37,42,36)(23,28,31,29,33,44,32,46)(25,34,40,52,41,39,47,53)(30,43,38,45,50,51,49,48);(19,20)(22,24)(23,29)(25,39)(26,35)(27,37)(28,32)(30,48)(31,44)(33,46)(34,41)(36,42)(38,43)(40,53)(45,50)(47,52)(49,51);(22,25,26,40,27,41,42,47)(23,30,31,38,33,50,32,49)(24,34,35,52,37,39,36,53)(28,43,29,45,44,51,46,48)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18425);