Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61100 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C2×C17 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ G | |
2616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,30)(21,32)(22,26)(23,27)(24,28)(25,29)(31,46)(33,35)(34,47)(36,40)(37,49)(38,43)(39,45)(41,44)(42,48);(18,20)(19,21)(22,37)(23,32)(24,40)(25,33)(26,42)(27,35)(28,30)(29,36)(31,38)(34,44)(39,47)(41,48)(43,49)(45,46);(18,21)(19,20)(22,34)(23,35)(24,30)(25,36)(26,31)(27,32)(28,40)(29,33)(37,44)(38,42)(39,49)(41,46)(43,47)(45,48);(18,22)(19,26)(20,31)(21,34)(23,38)(24,41)(25,39)(27,43)(28,44)(29,45)(30,46)(32,47)(33,48)(35,42)(36,49)(37,40);(18,23,25,24)(19,27,29,28)(20,32,33,40)(21,35,36,30)(22,38,39,41)(26,43,45,44)(31,47,48,37)(34,42,49,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54088);