Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61053 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#525 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(24,32)(25,29)(26,39)(27,30)(28,34)(31,42)(33,50)(35,48)(36,53)(37,49)(38,46)(40,44)(41,47)(43,52)(45,51);(22,24,27,35)(23,28,30,44)(25,36,38,52)(26,40,42,34)(29,45,46,50)(31,48,39,32)(33,41,51,37)(43,49,53,47);(19,21);(22,25,27,38)(23,29,30,46)(24,33,35,51)(26,41,42,37)(28,43,44,53)(31,49,39,47)(32,50,48,45)(34,52,40,36);(23,30)(28,44)(29,46)(31,39)(32,48)(43,53)(45,50)(47,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54041);