Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19823 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3325 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
632 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(21,29)(24,30)(25,26)(27,33)(31,32)(34,35)(36,40)(37,44)(38,46)(39,42)(41,43)(45,48)(47,49);(18,19)(20,24)(21,25)(22,26)(23,29)(27,31)(28,32)(30,33)(34,36,39,38)(35,40,42,46)(37,43,45,47)(41,48,49,44);(18,20,22,28)(19,24,26,32)(21,27,29,33)(23,30,25,31)(34,37,39,45)(35,41,42,49)(36,43,38,47)(40,48,46,44);(19,25)(21,29)(23,26)(24,31)(27,33)(30,32)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12811);