Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11310 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #387 |
| 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)(18,19,23,29,24,27,22,28)(20,30,32,45,33,25,38,40)(21,26,37,44,35,42,36,43)(31,46,34,49,47,39,48,41);(18,20)(19,25)(21,34,35,48)(22,32)(23,38)(24,33)(26,41,42,49)(27,30)(28,40)(29,45)(31,36,47,37)(39,43,46,44);(18,21)(19,26,27,42)(20,31)(22,37)(23,36)(24,35)(25,39,30,46)(28,44,29,43)(32,48)(33,47)(34,38)(40,49,45,41)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4298);