Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#10682 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(18,19,21,23)(20,24,25,22)(27,30)(31,32)(34,35,39,40,38,43,37,42)(36,44,47,41,46,49,45,48);(18,20,21,25)(19,22,23,24)(26,27,28,30)(29,31,33,32)(35,40)(37,39)(41,44)(42,43)(45,47)(48,49);(27,31)(29,33)(30,32)(34,36,38,46)(35,41,43,48)(37,47,39,45)(40,44,42,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3670);