Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10356 |
| 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 | |
452 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)(26,27)(28,30)(29,32)(31,33)(34,35,37,40)(36,44,46,49)(38,43,39,42)(41,45,48,47);(18,20,21,25)(19,22,23,24)(35,40)(36,45)(38,39)(41,44)(46,47)(48,49);(27,30)(28,33)(31,32)(34,36,37,46)(35,41,40,48)(38,45,39,47)(42,49,43,44)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3344);