Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11313 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #388 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1443 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29,32,25)(21,33)(22,37)(23,28)(24,27)(26,35)(30,47,49,43)(31,41,38,42)(34,40,48,46)(36,45)(39,44);(18,20,22,31,24,32,23,38)(19,25,37,42,27,29,28,41)(21,34,35,30,36,48,39,49)(26,43,45,40,44,47,33,46);(18,21)(19,26,27,44)(20,30)(22,35)(23,39)(24,36)(25,40,29,46)(28,33,37,45)(31,48)(32,49)(34,38)(41,43,42,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4301);