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×#11314 |
| 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 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
548 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)(18,19,23,28,24,27,22,29)(20,30,32,41,34,25,33,42)(21,35,38,44,39,45,37,26)(31,43,36,46,47,49,48,40);(18,20,22,32,24,34,23,33)(19,25,29,42,27,30,28,41)(21,36,37,47,39,48,38,31)(26,43,45,46,44,49,35,40);(18,21)(19,26,27,44)(20,31)(22,37)(23,38)(24,39)(25,40,30,46)(28,35,29,45)(32,36)(33,48)(34,47)(41,49,42,43)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4302);