Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#20998 |
| 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 | |
1704 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)(18,19,23,28,24,29,22,27)(20,30,33,41,34,40,32,25)(21,35,36,26,38,42,37,43)(31,39,45,48,47,49,46,44);(18,20)(19,25,29,41)(21,31)(22,32)(23,33)(24,34)(26,39,43,49)(27,40,28,30)(35,44,42,48)(36,45)(37,46)(38,47);(18,21)(19,26)(20,31)(22,36)(23,37)(24,38)(25,39)(27,42)(28,35)(29,43)(30,44)(32,45)(33,46)(34,47)(40,48)(41,49);(18,22,24,23)(19,27,29,28)(20,32,34,33)(21,36,38,37)(25,40,41,30)(26,42,43,35)(31,45,47,46)(39,48,49,44)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13986);