Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#20519 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C22 | C22×C42×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle, prime radical | C23×C17 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23)(24,28)(25,29)(26,27)(30,31,33,36,34,37,40,43)(32,35,39,42,38,41,44,45);(18,19,21,20)(23,27)(28,29);(18,20,21,19)(22,24,26,25)(23,28,27,29)(32,38)(35,41)(39,44)(42,45);(22,25,26,24)(23,29,27,28)(30,32,33,39,34,38,40,44)(31,35,36,42,37,41,43,45)1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13507);