Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11182 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #397 |
| 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)(22,23,27,33,28,31,26,32)(24,34,37,45,38,29,36,46)(25,39,41,48,43,49,42,30)(35,51,52,44,53,47,40,50);(18,19)(20,21)(22,24,28,38)(23,29,31,34)(25,40,43,52)(26,37,27,36)(30,47,48,51)(32,46,33,45)(35,41,53,42)(39,44,49,50);(19,21)(22,25)(23,30,31,48)(24,35)(26,41)(27,42)(28,43)(29,44,34,50)(32,39,33,49)(36,52)(37,40)(38,53)(45,47,46,51)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4170);