Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13442 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2054 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
398 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)(19,26)(20,32)(21,37)(22,23)(24,38)(28,41)(29,31)(30,39)(33,42)(34,48)(35,40)(36,46)(43,47)(45,49);(18,19)(20,33)(21,28)(22,29)(23,39)(24,41)(25,31)(26,37)(27,34)(30,38)(32,43)(35,49)(36,45)(40,44)(42,48)(46,47);(18,20,21,34,38,48,22,32,25,36,23,40,24,35,37,46)(19,27,26,33,41,47,39,49,31,44,29,45,30,43,28,42)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6430);