Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C210 |
| direct product | C17×#60070 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | 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 | |
4892 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)(20,28,31,24)(21,25)(22,26)(23,27)(29,40,42,35)(30,41,44,36)(32,37)(33,38)(34,39)(43,48,49,46)(45,47);(18,20)(19,24)(21,29)(22,30)(23,31)(25,35)(26,36)(27,28)(32,42)(33,43)(34,44)(37,40)(38,46)(39,41)(45,49)(47,48);(18,21)(19,25)(20,29)(22,33)(23,32)(24,35)(26,38)(27,37)(28,40)(30,43)(31,42)(34,45)(36,46)(39,47)(41,48)(44,49);(21,32)(25,37)(29,42)(33,45)(35,40)(38,47)(43,49)(46,48);(18,22,23,34)(19,26,27,39)(20,30,31,44)(21,33,32,45)(24,36,28,41)(25,38,37,47)(29,43,42,49)(35,46,40,48)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53058);