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×#20521 |
| 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 | |
866 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)(30,31,35,38,34,37,43,33)(32,39,42,41,40,36,44,45);(18,19,21,20)(23,27)(28,29)(30,32,34,40)(31,36,37,39)(33,41,38,45)(35,42,43,44);(18,20,21,19)(22,24,26,25)(23,28,27,29)(31,37)(32,40)(33,38)(42,44);(22,25,26,24)(23,29,27,28)(30,33,43,37,34,38,35,31)(32,41,44,39,40,45,42,36)1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13509);