Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13008 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #481 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1874 |
| prime radical | C17×#3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G | |
516 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)(18,19,22,27,23,28,39,45,24,26,21,34,36,43,37,47)(20,29,32,42,33,44,38,41,31,48,30,46,40,49,35,25);(18,20)(19,25,26,41)(21,35)(22,38)(23,40)(24,31)(27,44,34,49)(28,46,43,42)(29,47,48,45)(30,37)(32,39)(33,36);(19,26)(21,22)(25,41)(28,43)(30,32)(35,38)(37,39)(42,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5996);