Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 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)(21,26)(22,38)(23,29)(24,28)(25,31)(27,35)(30,40)(33,43)(34,46)(36,44)(37,48)(39,45)(41,47)(42,49);(19,26)(20,33)(21,24)(22,23)(27,44)(28,31)(29,48)(32,47)(34,35)(36,39)(37,40)(41,42)(43,46)(45,49);(18,20,21,34,25,36,24,42)(19,27,28,45,31,47,26,43)(22,39,37,35,40,33,23,41)(29,46,30,32,48,49,38,44)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6405);