Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1310 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)(18,19,24,38,23,25,22,28)(20,29,37,26,32,40,30,39)(21,33,35,42,36,27,34,43)(31,44,45,48,46,49,47,41);(19,25)(20,30)(22,24)(26,40)(27,33)(29,39)(31,45)(32,37)(34,35)(41,49)(44,48)(46,47);(18,20)(19,26)(21,31)(22,37)(23,32)(24,30)(25,39)(27,41)(28,40)(29,38)(33,48)(34,45)(35,47)(36,46)(42,44)(43,49);(18,21)(19,27)(20,31)(22,35)(23,36)(24,34)(25,33)(26,41)(28,43)(29,44)(30,45)(32,46)(37,47)(38,42)(39,48)(40,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17409);