Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#23474 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| socle | C2×C17 | C2×#393 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(20,24)(21,31,34,25)(22,26)(23,27)(28,41,32,36)(29,37)(30,38)(33,44,46,39)(35,40)(42,49,45,47)(43,48);(18,20)(19,24)(21,32,34,28)(22,29)(23,30)(25,36,31,41)(26,37)(27,38)(33,45,46,42)(35,43)(39,47,44,49)(40,48);(18,21)(19,25)(20,28)(22,33)(23,34)(24,36)(26,39)(27,31)(29,42)(30,32)(35,46)(37,47)(38,41)(40,44)(43,45)(48,49);(18,22,23,35)(19,26,27,40)(20,29,30,43)(21,33,34,46)(24,37,38,48)(25,39,31,44)(28,42,32,45)(36,47,41,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16462);