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×#19866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C2×D8×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(19,24)(20,22)(25,32)(26,30)(27,31)(28,33)(34,35,39,42)(36,40,38,46)(37,44,45,48)(41,47,49,43);(18,19,23,26)(20,24,22,30)(21,28,29,32)(25,31,33,27)(34,36,39,38)(35,40,42,46)(37,43,45,47)(41,48,49,44);(18,20,23,22)(19,24,26,30)(21,27,29,31)(25,32,33,28)(34,37)(35,41)(36,43)(38,47)(39,45)(40,48)(42,49)(44,46);(18,21,23,29)(19,25,26,33)(20,27,22,31)(24,32,30,28)(34,36,39,38)(35,40,42,46)(37,43,45,47)(41,48,49,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12854);