Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13309 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13395 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #2034 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C23×C8×C17 ◁ G | |
422 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)(20,28)(21,32)(22,37)(23,26)(24,30)(25,35)(27,34)(29,44)(31,41)(33,40)(36,48)(38,45)(39,46)(42,49)(43,47);(24,39)(28,44)(40,43)(41,45);(18,20,22,38,23,29,34,31)(19,24,27,43,26,39,37,40)(21,33,35,46,36,47,49,30)(25,41,32,44,42,45,48,28)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6383);