Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11188 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #394 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
794 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)(18,19)(20,21)(22,23,27,32,28,31,26,43)(24,33,36,49,37,29,35,45)(25,38,41,47,42,48,40,30)(34,46,39,44,52,53,51,50);(22,24,28,37)(23,29,31,33)(25,39,42,51)(26,36,27,35)(30,46,47,53)(32,49,43,45)(34,40,52,41)(38,50,48,44);(19,21)(22,25)(23,30,31,47)(24,34)(26,40)(27,41)(28,42)(29,44,33,50)(32,38,43,48)(35,51)(36,39)(37,52)(45,53,49,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4176);