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×#25438 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
892 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)(24,35)(25,30)(26,41)(27,33)(28,34)(29,37)(31,42)(32,39)(36,50)(38,45)(40,44)(43,48)(46,52)(47,51)(49,53);(18,20,21,19)(22,24,27,37,28,25,39,38)(23,29,32,35,34,45,33,30)(26,36,42,51,43,40,53,52)(31,44,41,47,49,50,48,46);(19,20)(22,25)(23,30)(24,28)(26,36)(27,38)(29,32)(31,47)(33,45)(34,35)(37,39)(40,43)(41,50)(42,51)(44,48)(46,49)(52,53);(22,26,39,53,28,43,27,42)(23,31,33,48,34,49,32,41)(24,36,38,52,25,40,37,51)(29,44,30,46,45,50,35,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18426);