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×#61051 |
| 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 | |
2734 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)(28,35)(31,40)(33,46)(34,43)(36,42)(37,50)(38,44)(41,48)(45,51)(47,53)(49,52);(22,24)(23,28)(25,33)(26,34)(27,36)(29,41)(30,43)(31,42)(32,39)(35,40)(37,47)(38,49)(44,53)(45,52)(46,50)(48,51);(19,21)(22,25,27,38)(23,29,30,44)(24,33,36,49)(26,37,40,51)(28,41,43,53)(31,45,39,50)(32,46,42,52)(34,47,35,48);(24,34)(26,40)(28,42)(31,39)(32,43)(33,47)(35,36)(37,51)(41,52)(45,50)(46,53)(48,49);(23,30)(28,43)(29,44)(31,39)(32,42)(41,53)(45,50)(46,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54039);