Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#10582 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
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)(18,19,22,24)(20,25,21,23)(26,27,29,32)(28,33,30,31)(34,35)(36,37)(38,40)(39,41);(18,20,22,21)(19,23,24,25)(26,28,29,30)(27,31,32,33)(34,36,39,40)(35,37,41,38);(18,21,22,20)(19,23,24,25)(27,31)(28,30)(32,33)(35,36)(37,38)(40,41)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3570);