Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61060 |
| 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 | |
2686 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)(26,40)(27,30)(28,35)(31,41)(33,48)(34,44)(36,43)(37,51)(38,52)(39,46)(42,50)(45,49)(47,53);(22,24,27,36)(23,28,30,44)(25,37,39,33)(26,34,41,35)(29,45,46,42)(31,43,40,32)(38,50,53,49)(47,48,52,51);(19,21)(22,25,27,39)(23,29,30,46)(24,33,36,37)(26,38,41,53)(28,42,44,45)(31,47,40,52)(32,48,43,51)(34,49,35,50);(24,34)(26,41)(28,43)(31,40)(32,44)(33,49)(35,36)(37,50)(38,53)(42,51)(45,48)(47,52);(23,30)(28,44)(29,46)(31,40)(32,43)(42,45)(47,52)(48,51)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54048);