Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18445 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
848 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)(18,19)(20,27)(21,25)(22,30)(23,26)(24,28)(29,32)(31,33)(34,35,38,40)(36,42,44,49)(37,45,47,41)(39,46,48,43);(18,20,23,29)(19,24,26,33)(21,28,22,31)(25,32,30,27)(34,36,38,44)(35,39,40,48)(37,46,47,43)(41,49,45,42);(18,19)(20,24)(21,30)(22,25)(23,26)(27,28)(29,33)(31,32)(34,35)(36,39)(37,45)(38,40)(41,47)(42,46)(43,49)(44,48);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(35,40)(39,48)(41,45)(42,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11433);