Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11288 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C24 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #385 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
602 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)(22,23,26,31,27,30,39,45)(24,28,34,42,33,41,37,46)(25,29,36,44,35,43,38,47)(32,40,49,51,48,52,50,53);(18,19)(20,21)(22,24)(23,28,30,41)(25,32,35,48)(26,37)(27,33)(29,40)(31,46,45,42)(34,39)(36,50,38,49)(43,52)(44,53)(47,51);(19,21)(22,25)(23,29,30,43)(24,32,33,48)(26,38)(27,35)(28,40)(31,47,45,44)(34,50,37,49)(36,39)(41,52)(42,53)(46,51)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4276);