Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C2×C42 |
| direct product | C17×#7959 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C24×C17 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
634 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(26,27)(28,34,36,40)(29,32)(30,33)(31,35,38,41)(37,39);(18,19,21,25,22,24,20,23)(26,28)(27,31,33,38)(29,35)(30,36)(32,34,39,40)(37,41);(19,24)(23,25)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 947);