Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11320 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #397 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23)(24,32,35,45)(25,29)(26,30)(27,31)(28,34,42,39)(33,48,36,47)(37,43)(38,44)(40,46)(41,51,52,50)(49,53);(18,19)(20,21)(22,24,26,39,27,35,40,34)(23,28,30,45,31,42,46,32)(25,36,37,50,38,33,49,51)(29,41,43,48,44,52,53,47);(18,20,21,19)(22,25,26,37,27,38,40,49)(23,29,30,43,31,44,46,53)(24,33,34,50,35,36,39,51)(28,41,32,47,42,52,45,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4308);