Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24985 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#24985 |
| 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 | |
646 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)(20,32)(21,36)(22,26)(23,30)(24,29)(25,31)(27,39)(28,35)(33,48)(34,43)(37,45)(38,44)(40,46)(41,47)(42,49);(18,20,24,34,25,35,23,22)(19,26,30,28,31,43,29,32)(21,37,39,33,41,38,40,49)(27,44,36,48,46,45,47,42);(18,21)(19,27)(20,33)(22,38)(23,39)(24,40)(25,41)(26,42)(28,45)(29,36)(30,47)(31,46)(32,44)(34,37)(35,49)(43,48);(18,22,23,35,25,34,24,20)(19,28,29,26,31,32,30,43)(21,38,39,49,41,37,40,33)(27,45,36,42,46,44,47,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17973);