Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12711 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12714 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1781 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3487 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×2−1+4 ◁ G | |
974 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)(20,30)(21,33,35,44)(22,36,38,27)(23,28)(24,29)(25,32,41,37)(26,31,43,39)(34,47)(40,48)(42,45)(46,49);(18,20,24,23)(19,25,29,41)(21,31,35,39)(22,32,38,37)(26,40,43,47)(27,30,36,28)(33,46,44,42)(34,45,48,49);(18,21,24,35)(19,26,29,43)(20,31,23,39)(22,34,38,48)(25,40,41,47)(27,42,36,46)(28,44,30,33)(32,45,37,49)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5702);