Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#24986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | #2420 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ G | |
642 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)(20,31)(21,35)(22,26)(23,40)(24,29)(25,30)(27,38)(28,34)(32,41)(33,42)(36,43)(37,45)(39,44)(46,47)(48,49);(18,20,23,22,25,34,24,33)(19,26,29,31,30,42,40,28)(21,36,38,32,39,47,37,48)(27,43,35,49,45,46,44,41);(18,21)(19,27)(20,32)(22,36)(23,37)(24,38)(25,39)(26,41)(28,43)(29,44)(30,45)(31,46)(33,47)(34,48)(35,40)(42,49);(18,22,23,34,25,33,24,20)(19,28,29,26,30,31,40,42)(21,36,37,48,39,47,38,32)(27,43,44,41,45,46,35,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17974);