Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#23834 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | #2398 |
| prime radical | C17×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C8×C17 ◁ G | |
608 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)(20,29,32,42)(21,26)(22,27)(23,37)(24,28)(25,33,39,30)(31,43,46,48)(34,40)(35,41)(36,47)(38,45,49,44);(20,30,32,33)(21,34)(25,29,39,42)(26,40)(31,45,46,44)(35,36)(38,48,49,43)(41,47);(18,20)(19,25)(21,31)(22,30)(23,33)(24,32)(26,38)(27,42)(28,39)(29,37)(34,46)(35,44)(36,45)(40,49)(41,48)(43,47);(18,21,22,35,24,34,23,36)(19,26,27,41,28,40,37,47)(20,31,30,44,32,46,33,45)(25,38,42,48,39,49,29,43)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16822);