Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10690 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #401 |
| commutator, Frattini, cosocle | C25 | C23×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C25×C17 ◁ G | |
372 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)(20,29,32,41)(21,33,36,42)(22,26)(23,28)(24,31,40,47)(25,35,43,37)(27,38)(30,44,34,49)(39,46,48,45);(18,20)(19,24,28,41)(21,34,35,45)(22,32)(23,31)(25,39,43,44)(26,40,27,29)(30,36,46,37)(33,48,42,49)(38,47);(18,21)(19,25,26,42)(20,30,31,34)(22,35)(23,37)(24,39,29,44)(27,43,28,33)(32,46,47,45)(36,38)(40,49,41,48)425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3679);