Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C210 |
| direct product | C17×#60076 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C2×C17 | C23×C22⋊C4 |
| prime radical | C2×C17×#585 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×#41×C17 ◁ G | |
4812 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)(18,19,23,29,24,28,22,27)(20,30,32,43,33,25,37,39)(21,26,36,42,34,40,35,41)(31,44,46,49,45,38,47,48);(18,20)(19,25)(21,31)(22,32)(23,37)(24,33)(26,38)(27,39)(28,30)(29,43)(34,45)(35,46)(36,47)(40,44)(41,48)(42,49);(18,21)(19,26)(20,31)(22,35)(23,36)(24,34)(25,38)(27,41)(28,40)(29,42)(30,44)(32,46)(33,45)(37,47)(39,48)(43,49);(21,34)(26,40)(31,45)(35,36)(38,44)(41,42)(46,47)(48,49);(18,22,24,23)(19,27,28,29)(20,32,33,37)(21,35,34,36)(25,39,30,43)(26,41,40,42)(31,46,45,47)(38,48,44,49)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53064);