Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#20995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#386 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 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)(21,34,37,43)(22,27)(23,28)(24,29)(25,32)(26,35,42,36)(31,45,48,39)(33,40)(38,41)(44,47,49,46);(18,20,22,32,24,33,23,38)(19,25,28,30,29,41,27,40)(21,31,35,46,37,48,36,47)(26,39,43,44,42,45,34,49);(18,21)(19,26)(20,31)(22,35)(23,36)(24,37)(25,39)(27,34)(28,43)(29,42)(30,44)(32,46)(33,48)(38,47)(40,49)(41,45);(18,22,24,23)(19,27,29,28)(20,32,33,38)(21,35,37,36)(25,40,41,30)(26,34,42,43)(31,46,48,47)(39,49,45,44)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13983);